§
§
BANSALCLASS
BANSALCLASSES
ES
TARGET
TARGET
IIT JEE 2007
IIT JEE
2007
XII (ALL)
XII (ALL)
QUESMOa MMEJM
QUESMOa MMEJM
MODERN
QUESTION
QUESTION FORFOR SHORT SHORT ANSWERANSWER
ATOMIC
ATOMIC PHYSICSPHYSICS
Q.
Q. l l In In thethe photoelectric effect, photoelectric effect, why why does does the the existence existence of of aa cu cutoff toff frequency frequency speak speak in in favour favour of of thethe photon photon theory
theory and and against against thethe wave theory? wave theory? Q.
Q. 22 ExplainExplain the the statement that on statement that one's eyes coulde's eyes could not not detect detect faint starlighfaint starlightt if if li light weght werere not not particle-like. particle-like. Q.
Q. 3 3 How How can can aa photon energy photon energy be be given given by E = by E = h/when h/when thethe very presence very presence of of thethe frequency/in frequency/in thethe formula formula implies that light
implies that light is a is a wave? wave? Q.
Q. 4 4 TheThe momentum p momentum p of of aa photon photon is is given given by p = by p = h h
IIX
X..
Why Why i iss it it that c, that c, the the speed oflight, does speed oflight, does not not appear appear in in this expression?this expression?
Q. 5
Q. 5 Given thatGiven that E = E = h/'for h/'for a a photon, photon, the the Doppler shift Doppler shift in in frequency frequency of of radiation froradiation fromm a a receding ligh receding light sout sourcerce would seem to indicate
would seem to indicate a a reduced energy reduced energy for the for the emitted photons. emitted photons. Is Is this this in in fact true? fact true? If so,If so, what happened what happened to the
to the conservation conservation of of energy energy principle?principle? Q.
Q. 6 6 AnyAny series series of of atomi atomic hc hydrogenydrogen yet to be yet to be observed will probably observed will probably bebe found found in in what region what region of of thethe spectrum? spectrum? Q.7
Q.7 Can Can aa hydrogen atom absorb hydrogen atom absorb a a photon whose energy exceeds photon whose energy exceeds its its binding energy( binding energy( 13.6 e13.6 eV)?V)? Q.
Q. 88 OnlyOnly a a relatively small number relatively small number of of Balmer lines Balmer lines can be can be observed from observed from laboratory discharge tublaboratory discharge tubes, whereases, whereas aa large number large number are are observed observed in in stellar spectra. Explain this stellar spectra. Explain this in in terms terms ofof thth e e smsmall deall densinsity, high temperature,ty, high temperature, and
and large volume large volume of of gases gases in in stellar atmospheres. stellar atmospheres. Q.
Q. 99 WnatWnat is the is the origin origin of of thethe cutoff cutoff wavelengthwavelength X Xmm mm of of figure figure shown?shown? Why is it an Why is it an important clue important clue to the to the photon photon
nature
nature of of xx rays? rays?
eeuu aa < <uu>> 30 40 50 60 70 80 90 30 40 50 60 70 80 90 Wavelength Wavelength (pm) (pm) Q. 10
Q. 10 CanCan atomic hydrogen atomic hydrogen be be caused caused to to emit emit x x rays? rays? If If so,so, describe describe how. how. Ifnot, Ifnot, why why not? not? Q.
Q. lll l Why Why is is itit that that B B ohr ohr theory, which does theory, which does not not work work very well evenvery well even for for helium (Z helium (Z = = 2), gives such 2), gives such a a good good account
account of of thethe characteristic x-ray spectra characteristic x-ray spectra of of thethe elements, elements, or at or at least least of of that pothat portion that rtion that originateoriginates deeps deep within
within thethe atom? atom? Q.12 The
Q.12 The ionization potential ionization potential of of hydrogen hydrogen is 13.6 is 13.6 V V.. Yet to Yet to obtain discharge obtain discharge in ain a cathode cathode ray ray tube tubefilledfilledwithwith hydrogen,
hydrogen, aa very hig very high voltage ( ~h voltage ( ~101044V) hasV) has to be to be applied across applied across the the tube. Explain this clearly. Also tube. Explain this clearly. Also
explain
explain why the gas why the gas must must be at low be at low pressure pressure to to obtain discharge. obtain discharge.
(fe
QUESTION
QUESTION FORFOR SHORT SHORT ANSWERANSWER
ATOMIC
ATOMIC PHYSICSPHYSICS
Q.
Q. l l In In thethe photoelectric effect, photoelectric effect, why why does does the the existence existence of of aa cu cutoff toff frequency frequency speak speak in in favour favour of of thethe photon photon theory
theory and and against against thethe wave theory? wave theory? Q.
Q. 22 ExplainExplain the the statement that on statement that one's eyes coulde's eyes could not not detect detect faint starlighfaint starlightt if if li light weght werere not not particle-like. particle-like. Q.
Q. 3 3 How How can can aa photon energy photon energy be be given given by E = by E = h/when h/when thethe very presence very presence of of thethe frequency/in frequency/in thethe formula formula implies that light
implies that light is a is a wave? wave? Q.
Q. 4 4 TheThe momentum p momentum p of of aa photon photon is is given given by p = by p = h h
IIX
X..
Why Why i iss it it that c, that c, the the speed oflight, does speed oflight, does not not appear appear in in this expression?this expression?
Q. 5
Q. 5 Given thatGiven that E = E = h/'for h/'for a a photon, photon, the the Doppler shift Doppler shift in in frequency frequency of of radiation froradiation fromm a a receding ligh receding light sout sourcerce would seem to indicate
would seem to indicate a a reduced energy reduced energy for the for the emitted photons. emitted photons. Is Is this this in in fact true? fact true? If so,If so, what happened what happened to the
to the conservation conservation of of energy energy principle?principle? Q.
Q. 6 6 AnyAny series series of of atomi atomic hc hydrogenydrogen yet to be yet to be observed will probably observed will probably bebe found found in in what region what region of of thethe spectrum? spectrum? Q.7
Q.7 Can Can aa hydrogen atom absorb hydrogen atom absorb a a photon whose energy exceeds photon whose energy exceeds its its binding energy( binding energy( 13.6 e13.6 eV)?V)? Q.
Q. 88 OnlyOnly a a relatively small number relatively small number of of Balmer lines Balmer lines can be can be observed from observed from laboratory discharge tublaboratory discharge tubes, whereases, whereas aa large number large number are are observed observed in in stellar spectra. Explain this stellar spectra. Explain this in in terms terms ofof thth e e smsmall deall densinsity, high temperature,ty, high temperature, and
and large volume large volume of of gases gases in in stellar atmospheres. stellar atmospheres. Q.
Q. 99 WnatWnat is the is the origin origin of of thethe cutoff cutoff wavelengthwavelength X Xmm mm of of figure figure shown?shown? Why is it an Why is it an important clue important clue to the to the photon photon
nature
nature of of xx rays? rays?
eeuu aa < <uu>> 30 40 50 60 70 80 90 30 40 50 60 70 80 90 Wavelength Wavelength (pm) (pm) Q. 10
Q. 10 CanCan atomic hydrogen atomic hydrogen be be caused caused to to emit emit x x rays? rays? If If so,so, describe describe how. how. Ifnot, Ifnot, why why not? not? Q.
Q. lll l Why Why is is itit that that B B ohr ohr theory, which does theory, which does not not work work very well evenvery well even for for helium (Z helium (Z = = 2), gives such 2), gives such a a good good account
account of of thethe characteristic x-ray spectra characteristic x-ray spectra of of thethe elements, elements, or at or at least least of of that pothat portion that rtion that originateoriginates deeps deep within
within thethe atom? atom? Q.12 The
Q.12 The ionization potential ionization potential of of hydrogen hydrogen is 13.6 is 13.6 V V.. Yet to Yet to obtain discharge obtain discharge in ain a cathode cathode ray ray tube tubefilledfilledwithwith hydrogen,
hydrogen, aa very hig very high voltage ( ~h voltage ( ~101044V) hasV) has to be to be applied across applied across the the tube. Explain this clearly. Also tube. Explain this clearly. Also
explain
explain why the gas why the gas must must be at low be at low pressure pressure to to obtain discharge. obtain discharge.
(fe
Q.13
Q.13 X-rays X-rays are are produced when produced when a a fast electron hits fast electron hits a a proper target. What happens proper target. What happens to the to the electron? electron?
Q.14 Why
Q.14 Why does does the the tail tail of of aa comet always point away from comet always point away from the the sun? sun?
Q.15 A
Q.15 A neutron pion neutron pion atat rest decays into rest decays into two two gamma photons. gamma photons. 7t° —-> y + y
7t° —-> y + y
Why
Why cannot cannot a a singl single phote photonon be be born? What conservation born? What conservation law is in law is in contradiction with contradiction with it? it?
Q.16
Q.16 What What is so is so special about special about e/m e/m rather than e rather than e end m end m separately? separately?
Q.1
Q.17 7 Why Why is is itit advisable advisable to to view view a TV a TV screen from screen from a a distance distance of of about about ten ten feet? feet? Q. 18
Q. 18 TheThe electrical conductivity electrical conductivity of a gas of a gas increases when X-rays increases when X-rays or or y-rays pass through it. Explain this y-rays pass through it. Explain this pheno
phenomenonmenon..
Q.19 In
Q.19 In photoelectric photoelectric emission exchangeemission exchange of of energy energy takes place among... takes place among... (phot(photonon a andnd electro electron/' photon, n/' photon, electronelectron and
and lattice). lattice).
Q.20 The
Q.20 The thresh threshold frequenciold frequencieses for for photoemission photoemission for for three metals numbered three metals numbered 1,2,3 are 1,2,3 are respectively respectively v v p p v v vv33
and
and V Vjj > v > v22 > > v v33.. An An incident radiation incident radiation of of frequency frequency v v00 > v > v22... cause photoemission cause photoemissionfromfrom3 but... cause3 but... cause
photoemission
photoemissionfromfrom1 (fill1 (fill in the in the gaps wit gaps with mayh may,, may not /may not / wil will certainly).l certainly).
NUCLEAR
NUCLEAR PHYSICSPHYSICS
Q. 1
Q. 1 WhyWhy does does the the relative importance relative importance of of thethe Coulomb force compared Coulomb force compared to the to the str strong nuclear ong nuclear forforce increasece increase at large mass numbers?
at large mass numbers?
Q.2 In
Q.2 In your body, your body, are are there mor there more neutrons than protons? More proe neutrons than protons? More protons than electrons? Discutons than electrons? Discussss
Q.
Q. 3 3 Why Why is is thethe binding energy binding energy per per nucleon nucleon (see (seefigure)figure)low at lowlow at low mass numbers? mass numbers? AtAt high mass numbers? high mass numbers? Region
Region of of greatest greatest r-^stability
r-^stability Jnisiqp
Jnisiqp FissionFission —i —ii.i... ~ ~55 BBr r 120* 120* f f ii VV ii j j !!22HH .... i i —— ' ' 11 0 0 20 20 4040 60 60 8080 100 120 MO 1100 120 MO 16161) 180 200 220 24) 180 200 220 24 00 Mass number, Mass number, AA Q.4
Q.4 Aradioactive Aradioactive nuclenucleusus ca cann emit emit a a positron, e positron, e++. This corresponds. This corresponds to ato a proton proton in the in the nucleus being converted nucleus being converted to a to a
neutron
neutron The The mass mass of of aa neutronneutron, however,, however, i iss greater than that greater than that o of f aa proton. proton. How How thai thai cancan positron emission occur? positron emission occur? Q.5 In
Q.5 In beta decay beta decay the the emitted electrons form emitted electrons form a a continuous spectrum, continuous spectrum, but in but in alpha decay alpha decay thethe alpha particles alpha particles form
form a a discrete spectrum. discrete spectrum. What What difficudifficultieslties di didd this cause this cause in the in the explanation explanation of of beta beta decaydecay,, and how and how were were these difficulties
these difficultiesfinallyfinallyovercome?overcome?
(fe
Q.6 How do neutrinos differ fro m photons? Each has zero charge and (presumably) zero rest mass and travels at the speed oflight.
Q.7 In radioactive dating with2 3 8U, how do you get around the fact that you do not know how much 2 3 8U
was present in the rocks to begin with? (Hint: What is the ultimate decay product of 2 38U?)
Q.8 If it is so much harder to get a nucleon out of a nucleus than to get an electron out of an atom, why try? Q.9 In the generalized equation for thefissiono f 2 3 5U by thermal neutrons, 2 3 5U + n -> X + Y + bn, do you
expect the Q of the reaction to depend on the identity of X and Y?
Q.10 The half-life of 2 3 5U is 7.0 x 108y. Discuss the assertion that ifit had turned out to be shorter by a factor
of 10 or so, there would not be any atomic bombs today.
Q.ll The binding energy curve of figuretells us that any nucleus more massive than A « 5 6 can release energy by the fission process. Only very massive nuclides seem to do so, however. Why cannot lead, for
example, release energy by the fission process?
Region of greatest ^"stability J - ' u s i q p F i s s i o n " ' " J r 5
Bp
B r I20g 2 3 9P u 74H e 1 I 5 7f l c ' ^ A u • H . . i i — i——i——i——i— 0 20 40 60 80 1 00 120 140 160 180 200 220 240 Mass number, AQ.12 Elements up to mass number w 5 6 are created by thermonuclear fusion in the cores of stars. Why are heavier elements not also created by this process?
Q.13 Which would generate more radioactive waste products: - afissionreactor or a fusion reactor? Q. 14 How can Becquerel rays, i.e., the combination of a- , P- and y-rays, be separated?
Q.15 When a nucleus undergoes a-decay, is the product atom electrically neutral? In (3-decay?
Q.16 Experimental results in radioactivity show small variations from the results predicted by theory. Explain this.
Q.17 If a nucleus emits only a y-rays photon, does its mass number change? Does its mass change?
ONLY ONE OPTION IS CORRECT. Take approx. 2 minutes for answering each question.
Q. 1 Let nr and n b be respectively the number of photons emitted by a red bulb and a blue bulb of equal
power in a given time.
£ (A)nr = n b ( B ) nr < n b ( C ) nr > n b (D) data insufficient
Q.2 10~3 W of 5000 A light is directed on a photoelectric cell. If the current in the cell is 0.16 pA, the
percentage of incident photons which produce photoelectrons, is
(A) 0.4% (B) .04% (C) 20% (D) 10%
£
Q.3 A proton and an electron are accelerated by same potential difference have de-Broglie wavelength
X
p and A,e.(A)
X
e= X
p (B) < (C)X
e>
X p (D) none of these.Q ,4 Two electrons are moving with the same speed v. One electron enters a region of uniform electric field while the other enters a region of uniform magneticfield,then after sometime ifthe de-Broglie wavelengths of the two are
X
{ andX
2,
then:(A) = X 2 (B)Aj > X 2 (C) X l < X 2 (D) X 1 > X 2 or X l < X 2
Q.5 In a photo-emissive cell, with exciting wavelength
X,
the maximum kinetic energy of electron is K. If the3X
exciting wavelength is changed to — the kinetic energy of the fastest emitted electron will be:
£
(A) 3K/4 (B) 4K/3 (C) less than 4K/3 (D) greater than 4K/3 Q.6 If the frequency of light in a photoelectric experiment is doubled, the stopping potential will
(A) be doubled (B) halved
(C) become more than doubled (D) become less than double
Q.7 An electron with initial kinetic energy of 100 eV is acceleration through a potential difference of 5 0 V Now the de-Broglie wavelength of electron becomes
^ ( A ) l A ( B ) V L 5 A (C) V3 A (D) 12.27 A
Q.8 If h is Planck's constant is SI system, the momentum of a photon of wavelength 0.01 A is: (A) 10"2 h (B)h ( C ) 1 02h ^(D) 101 2h
Q. 9 The stopping potential for the photo electrons emitted from a metal surface of work function 1.7 eV is 10.4 V. Identify the energy levels corresponding to the transitions in hydrogen atom which will result in emission of wavelength equal to that of incident radiation for the above photoelectric effect
(A)n = 3 to 1 (B)n = 3 to 2 ( C ) n = 2 t o l (D) n = 4 t o l
Q.10 When a photon of light collides with a metal surface, number of electrons, (if any) coming out is (A) only one (B) only two (C) infinite (D) depends upon factors
£
Q. 11 Two radioactive material Aj and ^ have decay constants of 10
X
0 andX
0.
If initially they have same number of nuclei, the ratio of number of their undecayed nuclei will be (1/e) after a timeL 1 1
(
A) r
^ ^
(
c> i s :
1dl Bansal Classes
Question Bank
on Modern Physics
i
£
Q.12 The frequency and the intensity of a beam oflig ht falling on the surface of photoelectric material are increased by a factor of two. This will:
(A) increase the maximum energy of the photoelectrons, as well as photoelectric current by a factor of two.
(B) increase the maximum kinetic energy of the photo electrons and would increase the photoelectric current by a factor of two.
(C) increase the maximum kinetic energy of the photoelectrons by a factor of greater than two and will have no effect on the magnitude of photoelectric current produced.
(D) not produce any effect on the kinetic energy of the emitted electrons but will increase the photoelectric current by a factor of two.
Q J o Light comingfroma discharge tubefilledwith hydrogen falls on the cathode of the photoelectric cell. The work function of the surface of cathode is 4eV Which one of the following values of the anode voltage (in Volts) with respect to the cathode will likely to make the photo current zero.
(A) - 4 ( B) -6 (C) - 8 (D )- 10
Q. 14 A point source of ligth is used in a photoelectric effect. If the source is removed farther fromthe emitting metal, the stopping potential:
(A) will increase (B) will decrease
(C) will remain constant (D) will either increase or decrease.
QJ/5 A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal ?
(A) (B) (C) (D)
Q.16 Let Kj be the maximum kinetic energy of photoelectrons emitted by a light of wavelength A, and K 2
corresponding to X2. If
= 2
"k 2, then:(A) 2Kj = K 2 (B) K, - 2K 2 ( C ) K , < | (D) K, > 2K 2
Q. 17 In a photoelectric experiment, the potential difference V that must be maintained betweenthe illuminated surface and the collector so as just to prevent any electron from reaching the collector is determined for differentfrequenciesf of the incident illumination. The graph obtained is shown.
The maximum kinetic energy of the electrons emitted atfrequencyf, is Vi
(B) 7fT3i
(A) iff. ( C ) h ( f 1- f 0) ( D ) e V1( f 1- f 0)
M v^ ( f i - f o )
Q.18 Radiation oftwo photon energies twice andfivetimes the work function of metal are incident sucessively on the metal surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be
(A) 1 :2 (B )2 . 1 (C) 1 4 (D )4 : 1
Q.19 Cut off potentials for a metal in photoelectric effect for light of wavelength Xx,X2 and X3 is found to be
Vj, V2 and V3 volts if Vj, V2 and V3 are inArithmetic Progression and A,,, X2 and A3 will be:
(A) Arithmetic Progression (B) Geometric Progression (C) Harmonic Progression (D) None
Q. 20 Photons with energy 5 eV are incident on a cathode C, on a photoelectric cell. The maximum energy of the emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons C will reach the anode A if the stopping potential of A relative to C is
(A)3 V ( B ) - 3 V ( C ) - 1 V (D) 4 V
Q.21 In a photoelectric experiment, the collector plate is at 2.0V with respect to the emitter plate made of copper cp - 4.5eV). The emitter is illuminated by a source of monochromatic light ofwavelength 200nm. (A) the minimum kinetic energy ofthe photoelectrons reaching the collector is 0.
(B) the maximum kinetic energy of the photoelectrons reaching the collector is 3,7eV. p (C) if the polarity of the battery is reversed then answer to part A will be 0.
(D) if the polarity of the battery is reversed then answer to part B will be 1,7eV.
Q.22 By increasing the intensity of incident light keepingfrequency(v > v0)fixedon the surface of metal
(A) kinetic energy of the photoelectrons increases (B) number of emitted electrons increases
(C) kinetic energy and number of electrons increases (D) no effect
Q.23 In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I and frequency f. The potential difference V required to stop the electrons is measured for various frequencies. If Y has a greater work function than X; which one of the following graphs best illustrates the expected results? V Vi X / /
<
(B)
f o V X (C) 0 V 4 (D) •f o Y /Q. 2,4 Monochromatic light with a frequency well above the cutoff frequency is incident on the emitter in a photoelectric effect apparatus. The frequency of the light is then doubled while the intensity is kept
constant. How does this affect the photoelectric current? (A) The photoelectric current will increase.
(B) The photoelectric current will decrease.
(C),The photoelectric current will remain the same. (D) None of these
Q. 2 5 In a hypothetical system a particle of mass m and charge - 3 q is moving around a very heavy particle having cahrge q. Assuming Bohr's model to be true to this system, the orbital velocity of mass m when it is nearest to heavy particle is
3q2 3q2 3q 3q
Q. 26 de-Broglie wavelength of an electron in the nth B ohr orbit is \ and the angular momentum is Jn, then:
" (A) Jn x (B)
l
noc
7~ (C)X
ncc
j2 (D) none of these** rt
q s * cvr\i f
Q.27 The angular momentum of an electron in the hydrogen atom is — . Here h is Planck's constant. The
\ 2tc
kinetic energy of this electron is:
(A)4.53 eV (B)1.51eV (C)3. 4eV (D)6.8eV
Q.28 Consider the following electronic energy level diagram of H-atom: Photons associated with shortest and longest wavelengths would be emitted from the atom by the transitions labelled:
(A) D and C respectively (B) C and A respectively A D C B - n = oo - n = 4 -n = 3 - n = 2 (C) C and D respectively n = j (D) Aand C respectively
Q.29 In a hydrogen atom, the binding energy of the electron in the nth state is E
n, then thefrquencyof revolutionof
the electron in the nth orbits is:
(A)2En/nh . (B) 2Enn/h (C)En/nh (D)Enn/h
Q.30 Ifthe electron in a hydrogen atom were in the energy level with n= 3, how much energy injoule would be required to ionise the atom? (Ionisation energy of H-atomis 2.18x 10""18J):
(A) 6.54 x 10 "19 (B) 1.43 x 10 "19 (C) 2.42 x 10~19 (D) 3.14x 10 "20
Q.31 In hydrogen and hydrogen like atoms, the ratio of difference of energies E4 n- E2 n and E2 n- En varies with
its atomic number z and n as:
( A ) z2/n2 (B) zVn4 (C )z /n (D)z°n°
Q.32 In a hydrogen atom, the electron is in nth excited state. It may come down to second excited state by . emitting ten different wavelengths. What is the value of n:
(A) 6 (B) 7 (C) 8 (D) 5
Q.33 Difference between nth and (n+1 )th Bohr's radius of'H' atom is equal to it's (n-1 )th Bohr's radius, the value ofnis:
(A) 1 (B) 2 (C) 3 (D) 4
Q.34 An electron in hydrogen atom after absorbing energy photons canjump between energy states nt and
n2(n, > nj). Then it may return to ground state after emitting six different wavelengths in emission spectrum.
| the energy of emitted photons is either equal to, less than or greater than the absorbed photons. Then nj and n2 are:
(A) n2 = 4, n} = 3 (B)n2 = 5 , n j = 3 (C)n2 = 4, n, = 2 (D) n2 = 4 , ^ = 1
Q.35 The electron in a hydrogen atom makes transitionfromM shell to L. The ratio of magnitudes of initial to final centripetal acceleration of the electron is
(A) 9: 4 (B)81:16 (C )4 :9 (D)16:81
Q.36 The electron in a hydrogen atom makes a transition n, —> n2 whose nj and n2 are the principal quantum
numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is 1/27 of that in thefinalstate. The possible values of nt and n2 are
(A) nt= 4 , n2 = 2 ( 6 ) ^ = 3 , ^ = 1 ( 0 ) ^ = 8 , ^ = 1 ( 0 ) ^ = 6 , ^ = 3
Q.37 The radiu s of B ohr' sfirstorbit is a0. The electron in nt h orbit has a radiu s:
(A) na0 (B)a0/n (C)n2a0 (D)a0/n2
Q.38 The ionisation potential of hydrogen atom is 13.6 volt. The energy required to remove an electron from ^ the second orbit of hydrogen is:
(A) 3.4 eV (B)6.8e V (C)13 .6eV (D)27. 2eV
Q.39 Electron in a hydrogen atom is replaced by an identically charged particle muon with mass 207 times that of electron. Now the radius of K shell will be
(A) 2.56 x 10~3
A
(B) 109.7A
(C) 1.21 x 10~3A
(D)22174.4AQ.40 Monochromatic radiation of wavelength
X
is incident on ahydrogen sample containing in ground state. Hydrogen atoms absorb the light and subsequently emit radiations of ten different wavelengths. The -value of X is(A) 95 nm (B)103nm (C) 73nm (D)8 8nm
Q.41 When a hydrogen atom, initially at rest emits, a photon resulting in transition n = 5 -> n = 1, its recoil speed is about
(A) 10^ m/s (B) 2 x 10"2 m/s (C) 4.2 m/s (D) 3.8 x l( T2 m/s
Q. 42 An electron collides with afixedhydrogen atom in its ground state. Hydrogen atom gets excited and the colliding electron loses all its kinetic energy. Consequently the hydrogen atom may emit a photon corresponding to the largest wavelength of the Balmer series. The min. K.E. of colliding electron will be (A) 10.2 eV (B) 1.9 eV (C)12. 1eV (D)13. 6eV
Q.43 Thefrequencyof revolution of electron in nt h Bohr orbit is v
n. The graph between log n and log (vn / v,)
may be
Q. 44 Consider the spectral line resulting from the transition n = 2 —» n = 1 in the atoms and ions given below. The shortest wavelength is produced by:
(A) hydrogen atom (B) deuterium atom
(C) singly ionized helium (D) doubly ionized lithium
Q.45 In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is: (neglect electric interaction)
(A) 1 : 4 (B) 4 : 1 (C) 1 : 8 (D) 8 : 1
Q.46 The electron in hydrogen atom in a sample is in nl h excited state, then the number of different spectrum
lines obtained in its emission spectrum will be:
(A) 1 + 2 + 3 + +(n - 1) (B) 1 + 2 + 3 + + ( n ) (C) 1 + 2 + 3 + +(n +1) (D) 1x 2 x 3 x x (
n _ l)
Q.47 The total energy of a hydrogen atom in its ground state is -13,6eV. If the potential energy in the first excited state is taken as zero then the total energy in the ground state will be :
<L (A) -3.4eV (B) 3.4 eV (C) -6. 8eV (D)6.8eV
Q. 48 A neutron collides head on with a stationary hydrogen atom in ground state (A) If kinetic energy of the neutronis less than 13.6eV, collisionmust be elastic (B) if kinetic energy of the neutron is less than 13,6eV, collision may be inelastic.
(C) inelastic collision takes place when initial kinetic energy of neutron is greater than 13. 6eV. (D) perfectly inelastic collision cannot take place.
Q. 49 The electron in a hydrogen atom make a transitionfroman excited state to the ground state. Which of the following statement is true ?
(A) Its kinetic energy increases and its potential and total energies decrease
(B) Its kinetic energy decreases, potential energy increases and its total energy remains the same. (C) Its kinetic and toal energies decrease and its potential energy increases.
(D) its kinetic potential and total energies decreases.
Q. 5 0 The magnitude of angular momentum, orbit radius and frequency of revolution of electron in hydrogen atom corresponding to quantum number n are L, r and f respectively Then according to Bohr's theory of hydrogen atom,
(A) fr 2L is constant for all orbits (B)frLis constant for all orbits
(C)
frL
is constant for all orbits (D) frL2 is constant for all orbitsQ.51 In a characteristic X- ray spectra of some atom superimposed on
continuous X- ra y spectra: f
(A) P represents K a line J
C (B) Q represents Kp line J
(C) Q and P represents K a and K p lines respectively J
(D) Relative positions of K a and K B depend on the particular atom
Q.52 The "K a" X-rays emission line of tungsten occurs at
X =
0.021 nm. The energy difference between Kand L levels in this atom is about
(A) 0.51 MeV (B) 1.2 MeV (C)5 9keV (D)13.6 eV
Q.53 Consider the nuclear reaction
X2 0 0 > A1 1 0 + B9 0
Ifth e binding energy per nucleon for X, AandB is7.4MeV, 8.2. MeV and 8.2 MeV respectively, what is the energy released ?
(A) 200 MeV (B) 160 MeV (C) 110 MeV (D) 90 MeV
Q. 54 The binding energy per nucleon for C1 2 is 7.68 MeV and that for C1 3 is 7.5 MeV The energy required
to remove a neutron from C1 3 is
(A) 5.34 MeV (B) 5.5 MeV (C) 9.5 Me V (D)9.34MeV
Q. 5 5 The binding energies of nuclei X and Y are EL and E2 respectively. Two atoms of X fuse to give one atom
of Y and an energy Q is released. Then:
(A) Q = 2 E j - E2 (B) Q = E2-2EJ (C) Q = 2 E J + E2 (D) Q = 2E2 + EJ
Q. 5 6 Radius of the second Bohr obit of singly ionised helium atom is
(A) 0.53
A
(B) 1.06A
(C) 0.265A
(D) 0.132A
Q. 5 7 An electron in Bohr's hydrogen atom has an energy of -3 .4 eV. The angular momentum of the electron is (A) h / 7i ' " (B) h / 2TC
(C) nh / ( n is an integer) (D) 2h/ 7t
Q.58 If each fission in a U2 3 5 nucleus releases 200 MeV, how many fissions must occurs per second to
produce a power of 1 KW
(A) 1.325 x 101 3 (B)3.125 x 101 3 (C) 1.235 x 101 3 (D) 2.135 x 101 3
Q.59 The rest mass of the deuteron, ] H, is equivalent to an energy of 1876 MeV, the rest mass of a proton is equivalent to 93 9 MeV and that of a neutron to 940 MeV. A deuteron may disintegrate to a proton and a neutron if it :
(A) emits a y - ray photon of energy 2 MeV (B) captures a y- ray photon of energy 2 MeV (C) emits a y-ray photon of energy 3 MeV (D) captures a y - ray photon of energy 3 MeV
Q.60 In an a-decay the Kinetic energy of a particle is 48 MeV and Q-value of the reaction is 5 0 MeV. The mass number of the mother nucleus is: (Assume that daughter nucleus is in ground state)
(A) 96 (B) 100 (C) 104 (D) none of these
Q.61 In the uranium radioactive series the initial nucleus is 9 2U2 3 8, and thefinalnucleus is 8 2P b2 0 6. When the
uranium nucleus decays to lead, the number ofa - particles emitted is.. and the number of (3-particles - emitted...
(A) 6, 8 (B) 8, 6 (C) 16, 6 (D) 32, 12
Q.62 The radioactive sources Aand B ofhalf lives o f2 hr and 4 hr respectively, initially contain the same number of radioactive atoms. At the end of 2 hours, their rates of disintegration are in the ratio :
( A ) 4 : l (B) 2 : 1 (C) V^: 1 (D) 1 : 1
Q.63 In a RA element the fraction of initiated amount remaining after its mean life time is 1
( A ) l - - ( B ) ^ (C) 1 (D) 1 - ~
e
Q. 64 90% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initialsample will decay in a total time 2t:
(A) 20% (B) 19% (C) 40% (D) 38%
Q.65 A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that producedfirsttime. If now their present activities are Aj and A2
respectively then their age difference equals:
t (B)T A, In—-A, In AA, T In A z 2A, (D)T l n A 2 2A, R, Q.66 Activity of a radioactive substance is Rj at time tj and R^ at time t2( t2 > t}). Then the ratio ^ is:
£
h( A ) - (B) e-Mtv+t2) (C)e
f \ - t ^ l l l 2
(D) eMti-t2)
Q.67 There are two radionuclei Aand B. Ais an alpha emitter and B is a beta emitter. Their distintegration constants are in the ratio of 1 : 2. What should be the ratio of number of atoms of two at time t = 0 so that probabilities of getting a and (3 particles are same at time t = 0.
(A) 2 : 1 (B) 1 : 2 (C) e (D) e"1
Q.68 The activity of a sample reduces from Aq to A()/ yr 3 inonehour. The activity after 3 hours more will be
A0 An Ao A0
2
<
A>i7?
w - f
Q.69 Halflife of radium is 1620years. How many radium nuclei decay in 5 hours in 5 gm radium? (Atomic weight of radium = 223)
(A) 9.1x 101 2 (B) 3.23 x 101 5 (C) 1.72 x 102 0 ( D ) 3 . 3 x l 01 7
Q. 70 Halflife for certain radioactive element is 5 min. Four nuclei of that element are observed at a certain instant of time. After fiveminutes
Assertion (A): It can be definitely said that two nuclei will be left undecayed.
Reasoning (R): After halflife i. e. 5 minutes, half of total nuclei will disintegrate. So onlytwo nuclei will be left undecayed. Then
(A) A is correct & R is correct explanation of A.
(B) Both are correct. But R is not correct explanation of A. (C) A is incorrect & Ris correct.
(D) Both are incorrect.
Q. 71 A certain radioactive nuclide of mass number m^ disintegrates, with the emission of an electron and y radiation only, to give second nuclied of mass number m^ Which one of the following equation correctly relates rr^ and my?
(A)my = mx+1 (B)my = mx-2 (C)my = m x- 1 ( D ) my = mx
Q.72 The number o f a and (3 "emitted during the radioactive decay chain starting from gg6Ra andendingat
^
I?
Pb is( A ) 3 a & 6 p - (B) 4 a & 5(3~ ( C ) 5 a & 4 p " ( D ) 6 a & 6 p "
Q.73 The activity of a sample of radioactive material is A, at time t, and .A, at time t2 (t2 >t,). Its mean life is T.
A -A
(A) Ajt, = A2t2 (B) = constant(C) A = A, j w r (D) = \ e(MTt2)
Q. 74 Afraction/ , of a radioactive sample decays in one mean life, and a fractionf 2 decays in one half-life.
(A)/, >/,
, ( B ) / , < / ;
/ (C)/ =f 2
(D) May be (A), (B) or (C) depending on the values of the mean life and halflife
Q.75 A radioactive substance is being produced at a constant rate of 10 nuclei/s. The decay constant of th e substance is 1/2 sec"1. After what time the number of radioactive nuclei will become 10? Initially there
are no nuclei present. Assume decay law holds for the sample.
1
(A) 2.45 sec (B) log(2) sec (C) 1.386 sec (D) sec
Q.76 The radioactivity o f a sample is R, at time Tj and R 2 at time T2. If the halflife of the specimen is T.
Number of atoms that have disintegrated in time (T2- Tj ) is proportional to
(A) ( R J , - R 2T2) (B) (Rj - R , ) T (C) (RJ -R, )/ T (D) ( Rj - R,) (Tt - T2)
Q. 77 The decay constant of the end product of a radioactive series is
(A) zero (B) infinite (C)finite(non zero) (D) depends on the end product. Q. 78 At time t = 0, N, nuclei of decay constant & N, nuclei of decay constant X2 are mixed . The decay
rate of the mixture is : (A) N1 N2e ~ ^1 + >"2^ (C) +(N1X1e "X l t+ N2A2e "X 2 t) V N2 7
(B) +
(D) +N1X] N2X2e (xrx2)tONE OR MORE THAN ONE OPTION MAY BE CORRECT Take approx. 3 minutes for answering each question.
Q.l In photoelectric effect, stopping potential depends on
(A) frequency of the incident light (B) intensity ofthe incident light byvaries source distance (C) emitter's properties (D)frequencyand intensity of the incident light
Q. 2 An electron in hydrogen atomfirst jumpsfromsecond excited state tofirstexcited state and then, from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons in the two cases be x, y and z, then select the wrong answer/(s):
(A )z= 1/x (B) x=9/4 (C) y=5/27 (D)z=5/27
Q.3 .An electron is in an excited state in hydrogen-like atom. It has a total energy of -3 .4 eV. If the kinetic energy ofthe electron is E and its de-Broglie wavelength is
X,
then(A) E = 6.8 eV, A, = 6.6 x 10"1 0m (B) E = 3.4 eV,
X
= 6.6 x l O -1 0m(C) E = 3.4 eV, X = 6.6x 10"11 m (D) E = 6.8 eV, X = 6.6 x 10"11 m
Q.4 A particular hydrogen like atom has its ground state binding "energy 122.4eV. Its is in ground state. Then:
(A) Its atomic number is 3
(B) An electron of 90eV can excite it.
(C) An electron of kinetic energy nearly 91 8eV can be brought to almost rest by this atom.
(D) An electron of kinetic energy 2.6eV may emerge from the atom when electron of kinetic energy 125eV collides with this atom.
Q.5 A beam ofultraviolet light of all wavelengths passes through hydrogen gas at room temperature, in the x-direction. Assume that all photons emitted due to electron transition inside the gas emerge in the y-direction. Let Aand B denote the lights emergingfromthe gas in the x and y directions respectively. (A) Some of the incident wavelengths will be absent in A.
(B) Only those wavelengths will be present in B which are absent in A. (C) B will contain some visible light.
(D) B will contain some infrared light.
Q.6 If radiation of allow wavelengthsfromultraviolet to infrared is passed through hydrogen agas at room temperature, absorption lines will be observed in the :
(A) Lyman series (B) Baimer series (C) both (A) and (B) (D) neither (A) nor (B)
Q.7 In the hydrogen atom, if the reference level of potential energy is assumed to be zero at the ground state level. Choose the incorrect statement.
(A) The total energy of the shell increases with increase in the value of n (B) The total energy of the shell decrease with increase in the value of n. (C) The difference in total energy of any two shells remains the same. (D) The total energy at the ground state becomes 13.6 eV.
Q. 8 Choose the correct statement(s) for hydrogen and deuterium atoms (considering motion of nucleus) (A) The radius of firstBohr orbit of deuterium is less than that of hydrogen
(B) The speed of electron in thefirstBohr orbit of deuterium is more than that of hydrogen. (C) The wavelength of firstBalmer line of deuterium is more than that of hydrogen
(D) The angular momentum of electron in thefirstBohr orbit of deuterium is more than that of hydrogen.
Q.9 Let An be the area enclosed by the nt h orbit in a hydrogen atom. The graph of In (An/A, ) agains In (n).
(A) will pass through origin
(B) will be a stright line will slope 4
(C) will be a monotonically increasing nonlinear curve (D) will be a circle.
Q, 10 A neutron collides head-on with a stationary hydrogen atom in ground state. Which of the following statements are correct (Assume that the hydrogen atom and neutron has same mass):
(A) If kinetic energy of the neutron is less than 20.4 eV collision must be elastic. (B) If kinetic energy of the neutron is less than 20.4 eV collision may be inelastic.
(C) Inelastic collision may be take place only when initial kinetic energy of neutron is greater than 20.4 eV. (D) Perfectly inelastic collision can not take place.
Q.ll When a nucleus with atomic number Z and mass number A undergoes a radioactive decay process: (A) both Z and A will decrease, if the process is a decay
(B) Z will decrease but A will not change, ifthe process is p+ decay
(C) Z will decrease but A will not change, if the process is (3~ decay (D) Z and A will remain unchanged, if the process is y decay.
Q.12 In a Coolidge tube experiment, the minimum wavelength of the continuous X-ray spectrum is equal to 66.3 pm, then
(A) electrons accelerate through a potential difference of 12.75 kV in the Coolidge tube (B) electrons accelerate through a potential difference of 18.75 kV inthe Coolidge tube (C) de-Broglie wavelength of the electrons reaching the anti cathode is of the order of 10pm. (D) de-Broglie wavelength of the electrons reaching the anticathode is 0.01
A.
Q.13 The potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation: (A) the intensity increases (B) the minimum wave length increases
(C) the intensity decreases (D) the minimum wave length decreases
Q.14 When the atomic number A of the nucleus increases (A) initially the neutron-proton ratio is constant = 1
(B) initially neutron-proton ratio increases and later decreases
(C) initially binding energy per nucleon increases and later decreases
(D) the binding energy per nucleon increases when the neutron-proton ratio increases.
Q.15 Let m p be the mass of a proton, mn the mass of a neutron, M, the mas of a ^ N e nucleus and M2 the
mass of a2[] Ca nucleus. Then
(A)M2 = 2M, (B) M2 > 2Mj (C) M2 < 2Mj (D) M, < 10(mn + m p)
Q.16 The decay constant of a radio active substance is 0.173 (years)"1. Therefore :
(A) Nearly 63% of the radioactive substance will decay in (1/0.173) year. (B) halflife of the radio active substance is (1/0.173) year.
(C) one -forth of the radioactive substance will be left after nearly 8 years. (D) all the above statements are true.
ANSWER KEY
ONLY ONE OPTION IS CORRECT.
Q i C Q.2 B Q.3 C Q 4 D Q.5 D Q.6 C Q.7 A Q.8 D Q.9 A Q.10 A Q. ll B Q.12 Q.13 D Q.14 C Q.15 D Q.16 C Q.17 C Q.18 A Q.19 C Q.20 B Q.21 B Q.22 B Q.23 A Q.24 B Q.25 A Q.26 A Q.27 B Q.28 C Q.29 A Q.30 C Q.31 D Q.32 A Q.33 D Q.34 C Q.35 D Q.36 B Q.37 C Q.38 A Q.39 A Q.40 A Q.41 C Q.42 C Q.43 C Q.44 D Q.45 C Q.46 B Q.47 C Q.48 A Q.49 A Q.50 B Q.51 C Q.52 C Q.53 B Q.54 A Q.55 B Q.56 B Q.57 A Q.58 B Q.59 D Q.60 B Q.61 B Q.62 C Q.63 C Q.64 B Q.65 C Q.66 D Q.67 A Q.68 B Q.69 B Q.70 D Q.71 D Q.72 C Q.73 C Q.74 A Q.75 C Q.76 B Q.77 A Q.78 C
ONE OR MORE THAN ONE OPTION MAYBE CORRECT
Q.l A,C Q 2 B Q.3 B Q 4 AC,D
Q.5 A,C,D Q.6 A Q.7 B Q.8 A
Q.9 AB Q.10 A,C Q.ll AB,D Q.12 B
TARGET
IIT JEE 2007
XII (ALL)
MODERN PHYSICS
C O N T E N T SKEYCONCEPTS
EXERCISE-I
EXERCISE-II
EXERCISE-III
ANSWER KEY
KEY CONCEPTS l. (a) (b) (c) 2. 3. 4. (0 (ii) (iii) (iv) (v) (vi) CATHODE RAYS :
Generated in a discharge tube in which a high vaccum is maintained . They are electrons accelerated by high p.d. (l Ot o 15 K.V.)
1 K.E. of C.R. particle accelerated by a p.d. V is — mv'
Can be deflected by Electric & magnetic fields . ELECTROMAGNETIC SPECTRUM Ordered arrangement of the big family
of electro magnetic waves (EMW) either in ascending order of frequencies or of wave lengths Speed ofE.M.W. in vacuum C = 3 x 108 m/s = v X 2m = eV. red(7.6xl0~7m) *— vioIet(3.6*l(r 7m) 3*104m 3m 3xl0^m 3xlO"l 2m
infrared Ultra viol et Ga mma rays
Radio waves
I I X-rays
Micro waves \
(e.g. radar) Visible light
104 106 10s 1 01 01 01 21 01 4 1016 I0i 81 02°
Frequency (Hz) PLANK
S
QUANTUM THEORY :A beam ofEMW is a stream of discrete packets of energy called PHOTONS ,
each photon having afrequencyv and energy = E = h v .
h = plank's constant = 6.63 x 10"34 Js .
PHOTO ELECTRIC EFFECT :
The phenomenon of the emission of electrons , when metals are exposed to light (of a certain minimum frequency) is called photo electric effect.
Results :
Can be explained only on the basis of the quantum theory (concept of photon).
Electrons are emitted ifthe incident light hasfrequencyv > vQ (thresholdfrequency)emission of electrons
is independent of intensity. The wave length corresponding to v0is called threshold wave length
X
0.
v0 is different for different metals .
Number of electrons emitted per second depends on the intensity of the incident light .
EINSTEINS PHOTO ELECTRIC EQUATION :
Photon energy = K.
E.
of electron + work function .1 2 ,
h v = — mv + <b
2
(j) =Work function = energy needed by the electron in freeing itself from the atoms of the metal . d> = h v0
STOPPING POTENTIAL O R C UT O F F PO TENTIAL :
The minimum value of the retarding potential to prevent electron emission is :
eVcutofr = ( K E) m a x
Note: The number of photons incident on a surface per unit time is called photon flux.
5. WAVE NATURE OF MATTER :
Beams of electrons and other forms of matter exhibit wave properties including interference and diffraction
with a de Broglie wave length given by
X = —
P (wave length of a praticle) .<i§Bansal Classes Modern Physics [11]
6. ATOMIC MODELS :
(a) THOMSON MODEL : (PLUM PUDDING MODEL)
(i) Most of the mass and all the positive charge of an atom is uniformly distributed over the full size of atom (1 0"1 0m).
(ii) Electrons are studded in this uniform distribution .
(iii) Failed to explain the large angle scattering a - particle scattered by thin foils of matter . (b) RUTHERFORD MODEL : (Nuclear Model)
(i) The most of the mass and all the positive charge is concentrated within a size of 10"14 m inside
the atom . This concentration is called the atomic nucleus .
(ii) The electron revolves around the nucleus under electric interaction between themin circular orbits. An accelerating charge radiates the nucleus spiralling inward and finally fall into the nucleus, which does not happen in an atom. This could not be explained by this model .
(c) BOHR ATOMIC MODEL :
Bohr adopted Rutherford model of the atom & added some arbitrary conditions. These conditions are known as his postulates :
(i) The electron in a stable orbit does not radiate energy .i.e. m V =
-r r
(ii) A stable orbit is that in which the angular momentum of the electron about nucleus
ll ll
is an integral (n) multiple of — . i.e. mvr = n — ; n = 1, 2 , 3 , (n * 0).
Z7C 271
(iii) The electron can absorb or radiate energy only if the electron jumpsfroma lower to a higher orbit or fallsfroma higher to a lower orbit .
(iv) The energy emitted or absorbed is a light photon of frequency v and of energy. E = hv . FOR HYDROGEN ATOM : (Z - atomic number = 1)
(i) L = angular momentum in the nt h orbit = n — .
2%
(ii) r n - radius of nt h circular orbit = (0.529 A0) n2 ; (1 A0 = 10"10 m); r n a n2.
(iii) En Energy of the electron in the nt h orbit = — e V i.e. En a .
Note: Total energy of th e electron in an atom is negative , indicating that it is bound . Binding Energy (BE) = - E = 1 3 , 6 e v .
n
(iv) En 2 - En l = Energy emitted when an electron jumps from n2t h orbit to n,t h orbit (n2 > nt) .
1 1
AE = (13.6 ev) 2 2
n , n2
AE = hv ; v = frequency of spectral line emitted .
— = v = wave no. [no. ofwaves in unit length (lm)] = R
A, ni 2 n2 2
Where R = Rydberg's constant for hydrogen = 1.097 x 107 m"1 .
(v) For hydrogen like atom/spicies of atomic number Z :
r
n 2 = ^ ^ n2 = (0.529A0) ^ ; E z = ( - 13.6) ^ ev
z Z n
R 7 = RZ2 - Rydberg's constant for element of atomic no. Z .
Note : If motion of the nucleus is also considered, then m is replaced by p. .
Where p = reduced mass of electron - nucleus system = mM/(m+M). 7. (0 00 9. 11. (0 (ii) (iii) (iv)
In this case E„ = (-13 .6 ev) — . —n. v 7 o
n2 me
SPECTRAL SERIES :
Lyman Series : (Landing orbit n = 1) .
v"=R i 2 1 12
1 n 2
Ultraviolet region
Balmer Series : (Landing orbit n = 2) 1 1 n2> 1 Visible region v = R 0 2 2 2 n 2 >2 (iii) Paschan Series : (Landing orbit n = 3)
In the near infrared region v = R
1 2 r, 2
3 n 2
n2 > 3
(iv) Bracket Series : (Landing orbit n = 4)
In the mid infrared region v = R 42
> 4
(v) Pfund Series : (Landing orbit n = 5)
In far infrared region v = R ^ > 5
In all these series n2 = n, + 1 is the a line
= n, + 2 is the P line
= n, + 3 is the y line etc . where n, = Landing orbit
EXCITATION PO TENTIAL OF ATOM :
Excitation potential for quantum jump from n} -» n2
electronch arg e IONIZATION ENERG Y :
The energy required to remove an electronfroman atom . The energy required to ionize hydrogen atom is = 0 - ( -1 3. 6) = 13.6 ev .
10. IONIZATION POTENTIAL :
Potential difference through which an electron is moved to gain ionization energy = -E.
electronicch arg e X-RAYS :
Short wavelength (0.1 A0 to 1 A0) electromagnetic radiation .
Are produced when a metal anode is bombarded by very high energy electrons .
Are not affected by electric and magnetic field . They cause photoelectric emission .
Characteristics equation eV = h vm
e = electron charge ; V = accelerating potential
v = maximum frequency of X - radiation
k u~ kp-Characteristic Spectrum
3ntiaous Spectrum
35000 volt
(v) Intensity of X - rays depends on number of electrons hitting the target .
(vi) Cut off wavelength or minimum wavelength, where v (in volts) is the p.d. applied to the tube X J * ! " A" .min -y
(vii) Continuous spectrum due to retardation of electrons.
(viii) Characteristic Spectrum due to transition of electronfromhigher to lower
v a ( z - b )2 ; u = a ( z - b ) 2 [ MOSELEY'S LAW ]
b = 1 for K series ; b = 7.4 for L series
Where b is Shielding factor (different for different series). Note : (i) Binding energy=- [ Total Mechanical Energy ]
(ii) Vel. of electron in nt h orbit for hydrogen atom = — ; c = speed oflig ht.
137n
(iii) For x - rays - -R (z -b )2
X
1 1
2 2
Vni n2 J
(iv) Series limit of series means minimum wave length of that series.
1 2. N U C L E A R D I M E N S I O N S :
R = R 0A1 / 3 Where R 0 = empirical constant = 1.1 x 10~15 m ; A = Mass number ofthe atom
1 3. R A D I O A C T I V I T Y :
The phenomenon of self emission of radiation is called radioactivity and the substances which emit these radiations are called radioactive substances . It can be natural or artificial (induced) .
1 4 . a . , p , y R A D I A T I O N :
(i) a - particle :
(a) Helium nucleus (2He4) ; (b) energy varies from 4 Mev to 9 Mev;
(c) Velocity 106 - 107 m/s ; (d) low penetration
(ii) p - particle :
(a) Have much less energy; (b) more penetration; (c) higher velocities than a particles (iii) y - radiation : Electromagnetic waves of very high energy .
1 5. L A W S O F R A D I O A C T I V E D I S I N T E G R A T I O N :
(A) DISPLACEMENT LAW : In all radioactive transformation either an a or p particle (never both or more
than one of each simultaneously) is emitted by the nucleus of the atom. (i) a-emissi on :ZXA ->Z _ 2YA _ 4 + 2a4 + Energy
(ii) P - emission : ZXA > P+ Z + 1YA+ v (antinuetrino)
(iii) y - emission : emission does not affect either the charge number or the mass number .
( B ) STASTISTICAL LAW : The disintegration is a random phenomenon. Whcih atom disintegrates first is
purely a matter of chance .
Number of nuclei disintegrating per second is given ; (disintegration /s /gm is called specific activity) .
0 dN X T dN ,X T
(i) — a N —>—=-A,N = activity . dt dt
Where N = No. of nuclei present at time t ;
X -
decay constant (ii) N = No e~ N0 = number of nuclei present in the beginning .(iii) Half life of the population T1 / 2 = •
A
N
at the end of n half-life periods the number of nuclei left N = — .
. . . . , Slifetimeof allatoms „ 1
( i v ) ME AN LIFE OF AN ATOM = ; T = —
totalnumberof atoms A
(v) CURIE : The unit of activity of any radioactive substance in which the number of disintegration
per second is 3.7 xlO1 0 .
16. ATOMIC MASS UNIT (a.m.u . OR U) :
1 amu = — x (mass of carbon-12 atom) = 1.6603 x 10~27 kg
17. MASS AND ENERGY :
The mass m of a particle is equivalent to an energy given by E = mc2 ;
c = speed of light. 1 amu = 931 Mev
18. MASS DEFECT AND BINDING ENERGY OF A NUCLEUS :
The nucleus is less massive than its constituents. The difference of masses is called mass defect .
A M = mass defect = [ ZM P + ( A - Z) m J - M ^ .
Total energy required to be given to the nucleus to tear apart the individual nucleons c om p o s i n g the nucleus, away from each other and beyond the range of interaction forces is called the Binding Energy of a nucleus .
B E . = ( A M ) C2.
( A M ) C2
B E. per nucleon = - — ~ — .
Greater the BE . , greater is the stability of the nucleus .
19. NUCLEAR FISSION :
(i) Heavy nuclei of A, above 20 0, break up onto two or more fragments of comparable masses. (ii) The total B.E. increases and excess energy is released .
(iii) The man point of the fission energy is leberated in the form of th e K.E. of th e fission fragments . eg. 29 2U+ on l^29 2U^I546B a+ 3 6K r +3on l + ^ S Y
20. NUCLEAR FUSION (The rmo nuclear reaction) :
(i) Light nuclei ofAbelow 20 , fuse together, the BE. per nucleon increases and hence the excess energy is released .
(ii) These reactions take place at ultra high temperature ( = 107 to 109)
(iii) Energy released exceeds the energy liberated in thefissionof heavy nuclei . eg. 4{P-»j1He+°
1e . (Positron)
(iv) The energy released in fusion is specified by specifying Q value . i.e. Q value of reaction = energy released in a reaction .
Note : (i) In emission of p", z increases by 1 . (ii) In emission of , z decreases by 1 .
EXERCISE
# I
Q.l A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of 200W/m2. The number of photons in 1mm3 of this radiation are
Q. 2 When photons of energy 4.25 eV strike the surface of a metal A, the ej ected photoelectrons have maximum kinetic energy Ta eV and de Broglie wavelength
X
a
.
The maximum kinetic energy of photoelectronsliberated from another metal B by photons of energy 4.7eV is T b = (T -1 .5 ) eV. If the De Broglie
wavelength of these photoelectrons is = 2
X
&
,
then find(a) The work function of a (b) The work function of b is (c) Ta and T b
Q.3 When a monochromatic point source oflight is at a distance of 0.2 mfroma photoelectric cell, the cut off voltage and the saturation current are respectively 0.6 volt and 18.0 mA. Ifth e same source is placed 0.6 m away from the photoelectric cell, then find
(a) the stopping potential (b) the saturation current
Q.4 An isolated metal body is illuminated with monochromatic light and is observed to become charged to a steady positive potential 1.0V with respect to the surrounding. The work function of the metal is 3 0 eV. The frequency of the incident light is .
Q. 5 663 mW oflight from a 540 nm source is incident on the surface of a metal. If only 1 of each 5 x 109
incident photons is absorbed and causes an electron to be ejectedfromthe surface, the total photocurrent in the circuit is .
Q. 6 Light of wavelength 330 nm falling on a piece of metal ej ects electrons with sufficient energy which requires voltage V0 to prevent a collector. In the same setup, light of wavelength 220 nm, ej ects electrons
which require twice the voltage V0 to stop them in reaching a collector. Find the numerical value of
voltage V0.(Take plank's constant, h = 6.6 x i c r 3 4 Js and 1 eV= 1.6 x 10~19 J)
Q.7 A hydrogen atom in a state having a binding energy 0.85eV makes a transition to a state of excitation energy 10.2eV. The wave length of emitted photon is nm.
Q.8 A hydrogen atom is in 5t h excited state. When the electron jumps to ground state the velocity of recoiling
hydrogen atom is m/s and the energy of the photon is eV.
Q. 9 The ratio of series limit wavlength ofBalmer series to wavelength of firstline of paschen series is
Q.10 An electron joins a helium nucleus to form a He+ ion. The wavelength ofthe photon emitted in this process if the electron is assumed to have had no kinetic energy when it combines with nucleus is nm.
Q.ll Three energy levels of an atom are shown in thefigure.The wavelength corresponding to three possible transition are A,,
X
2 and
X
y The valueE?
-o f X
3 in terms of A, andX
2 is given by .Xi x2
- n = 2
Q.12 Imagine an atom made up of a proton and a hypothetical particle of double the mass of an electron but having the same charge as the electron. Apply the Bohr atom model and consider a possible transitions of this hypothetical particle to the first excited level. Find the longest wavelngth photon that will be emitted
X
(in terms of the Rydberg constant R.)Q.13 In a hydrogen atom, the electron moves in an orbit of radius 0.5 A making 101 6 revolution per second.
The magnetic moment associated with the orbital motion of the electron is .
Q.14 The positron is a fundamental particle with the same mass as that ofthe electron and with a charge equal to that of an electron but of opposite sign. When a positron and an electron collide, they may annihilate each other. The energy corresponding to their mass appears in two photons of equal energy. Find the wavelength of the radiation emitted.
[Take : mass ofelectr on = (0.5/C2)MeVandhC= 1.2xlO~I2MeV.m where his the Plank's constant
and C is the velocity oflight in air]
Q.15 Asmall 10W source of ultraviolet light ofwavele ngth 99 nm is held at a distance 0.1 mfr om ame ta l surface. The radius of an atom ofthe metal is approximately 0.05 nm. Find
(i) the average number of photons strildng an atom per second.
(ii) the number ofphotoelectrons emitted per unit area per second ifthe efficiency ofliberation ofphotoelectrons is 1 %. Q.16 The surface of cesium is illuminated with monochromatic light of various
wavelengths and the stopping potentials for the wavelengths are measured. The results of this experiment is plotted as shown in thefigure.Estimate the value of work function of the cesium and Planck's constant.
Q.17 A hydrogen like atom has its single electron orbiting around its stationary nucleus. The energy to excite the electron from the second Bohr orbit to the third Bohr orbit is 47.2 eV. The atomic number of this
nucleusis .
Q.18 A single electron orbits a stationary nucleus of charge Ze where Z is a constant and e is the electronic charge. It requires 47.2eV to excite the electron from the 2nd Bohr orbit to 3rd Bohr orbit. Find (i) the value of Z,
(ii) energy required to excite the electronfromthe third to the fourth orbit
(iii) the wavelength of radiation required to remove the electronfromthefirstorbit to infinity (iv) the kinetic energy, potential energy and angular momentum in the first Bohr orbit
(v) the radius of thefirstBohr orbit.
Q .19 A hydrogen like atom (atomic number Z) is in higher excited state of quantum number n. This excited atom can make a transition to the first excited state by successively emitting two photons of energy 22.95 eV and 5.15eV respectively. Alternatively, the atomfromthe same excited state can make transition to the second excited state by successively emitting two photons of energies 2.4eV and 8.7eV respectively. Find the values of n and Z.
Q.20 Find the binding energy of an electron in the ground state of a hydrogen like atom in whose spectrum the third of the corresponding B aimer series is equal to 108. 5nm.
Q.21 Which level of the doubly ionized lithium has the same energy as the ground state energy of the hydrogen atom. Find the ratio ofth e two radii of corresponding orbits.
Q.22 The binding energies per nucleon for deuteron ( jH2) and helium (
2H e4) are 1.1 MeV and 7.0 MeV
respectively. The energy released when two deuterons fuse to form a. helium nucleus (2He4)is .
Q.23 Aradioactive decay counter is switched on at t = 0. A P - active sample is present near the counter. The counter registers the number of P - particles emitted by the sample. The counter registers 1 x 10'
P - particles at t = 36 s and 1.11 * 10s P - particles at t = 108 s. FindT, of this sample
Q.24 An isotopes of Potassium has a half life of 1.4 x 109 year and decays to Argon ^ A r which is stable.
(i) Write down the nuclear reaction representing this decay.
(ii) A sample of rock takenfromthe moon contains both potassium and argon in the ratio 1 /7. Find age of rock
Q.25 At t = 0, a sample is placed in a reactor. An unstable nuclide is produced at a constant rate R in the sample by neutron absorption. This nuclide P~~ decays with halflif e x. Find the time required to produce 80% of the equilibrium quantity of this unstable nuclide.
Q.26 Suppose that the Sun consists entirely of hydrogen atom and releases the energy by the nuclear reaction,
4
|H > ,H e with 26 MeV of energy released. Ifth e total output power of the Sun is assumed to remain constant at 3.9 x 1026 W,findthe time it will take to burn all the hydrogen. Take the mass of theSun as 1.7 x 103 0kg. f 2-1 f 2-1-0.41 I-.-7 1-2V 1.5 1.0 1.5 V I O '5H Z
Q. 27 Assuming that the source of the energy of solar radiation is the energy of the formation of helium from hydrogen according to the following cyclic reaction :
C'2 + ,H' 7 N1 3 X1 3 + e° 6 1 / o + l ,C1 3 + ,H' N1 4 0 1 / 7 N1 4 + ,H1 801 5 ->7 N1 5 ++1e° 7 N1 5 + ]H1 ->6C1 2 + 2He4
Find how many tons of hydrogen must be converted every second into helium . The solar constant is 8 J / cm2 min. Assume that hydrogen forms 35% of the sun's mass. Calculate in how many years this
hydrogen will be used up if the radiation of the sun is constant. me = 5.49 x 104 amu, atomic masses
m^l .0 081 4 amu, mHe=4.00388 amu, mass ofthe sun=2 x 1030 kg, distance between the sun and the
earth= 1.5* 10nm. 1 amu = 931 MeV.
Q. 28 An electron of mass "m" and charge "e" initially at rest gets accelerated by a constant electricfieldE. The rate of change of DeBroglie wavelength of this electron at time t is
List of recommended questions from I.E. Irodov.
5.247, 5.249, 5.260, 5.262, 5.263, 5.264, 5.265, 5.266, 5.270, 5.273, 5.277 6.21, 6.22, 6.27, 6.28, 6.30, 6.31, 6.32, 6.33, 6.35, 6.37, 6.38, 6.39, 6.40,
6.41, 6.42, 6.43, 6.49, 6.50, 6.51, 6.52, 6.53, 6.133, 6.134, 6.135, 6.136, 6.137, 6.138, 6.141, 6.214, 6.233, 6.249, 6.264, 6.289
EXERCISE # II
Q.l Find the force exerted by a light beam of intensity I, incident on a cylinder I (height h and base radius R) placed on a smooth surface as shown infigureif: • (a) surface of cylinder i s perfectly reflecting > (b) surface of cylinder is having reflection coefficient 0.8. (assume no »
transmission) t —
Q. 2 A small plate of a metal (work function =1.17 eV) is placed at a distance of 2mfroma monochromatic light source of wave length 4.8 * 10"7 m and power 1.0 watt. The light falls normally on the plate. Find
the number of photons striking the metal plate per square meter per sec. If a constant uniform magnetic field of strength A tesla is applied parallel to the metal surface. Find the radius of the
largest circular path followed by the emitted photoelectrons.
Q. 3 Electrons in hydrogen like atoms (Z = 3) make transitions from thefifthto the fourth orbit & from the fourth to the third orbit. The resulting radiations are incident normally on a metal plate & eject photo electrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is 3.95 volts. Calculate the work function of the metal, & the stopping potential for the photoelectrons ejected by the longer wavelength. (Rydberg constant = 1.094 x 107 m 1)
Q.4 A beam of light has three wavelengths 4144
A,
4972A
& 6216A
with a total intensity of 3.6x 10"3 W. m2 equally distributed amongst the three wavelengths. The beam falls normally on an area1.0 cm2 of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by
reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in two seconds.
