26.Electron & Photon

/

Electron

and Photon

Chapter Overview

Discovery of Cathode Rays (Eiedron) Positive Rays

" Photoelectric Effect

• Planck's Quantum Theory • Compton Effect

" Dual Character of Radiation

t

>

·

Discovery of Cathode

Rays (Electron)

Sir William Crooks studied various gases in a gas discharge tube (a glass tube with a very high potential applied to its ends) at low pressures. If the pressure in the tube is lowered to about 10-4 atm, glass begins to fluoresce (glow) faintly. It was established that the glow was due to bombardment of the glass by a certain kind of rays emerging from cathode (negative electrode) which travel in a straight line until they strike the anode (positive electrode). These rays were called as cathode rays.

Sir J J Thomson demonstrated that when cathode rays were deflected on to an electrometer, it acquired negative charge. He also showed that the rays were deflected on application of an electric field. The cathode ray beam was deflected away from the negatively charged plate. These results were found to be identical, irrespective of the gas taken in the discharge tube. He concluded that the cathode rays were a stream of fast moving negatively charged particles called electrons (named by stoney). He also calculated the velocity and specific charge for an electron. The specific charge is the ratio of charge to the mass of an electron, denoted as elm ratio. The elm ratio was found to be same for all gases. This led to the conclusion that the electron must be a fundamental or universal particle common to all kinds of the atoms. ·

988

Chapter 26

•

Electron

and

Photon

Properties of Cathode Rays

(i) Cathode rays travel in straight lines.

(ii) The cathode rays are independent of the nature of the gas or electrodes employed to produce them in the discharge tube. Therefore, .::_ for cathode rays is a

m

universal constant equal to 1. 7592 x 1011 C kg-1. (iii) They can be deflected by electric and magnetic fields. (iv) They have penetrating power and can penetrate through

small thickness of matter.

(v) On striking the target of high atomic weight and high m~lting point, they produce X-rays.

(vi) They produce fluorescence and phosphorescence in certain substances and hence affect photographic plate. (vii) They have small ionising power and ionise the gas

through which they pass.

(viii) They travel in straight line with high velocity, momentum and energy and cast shadow of objects placed in their path.

(ix) They emerge normally from surface of cathode and can therefore be brought to focus by using a concave cathode. (x) They heat up the material on which they fall.

(xi) They exerts mechanical pressure, so they can rotate a small paddle wheel.

(xii) They can produce physical and chemical change. (xiii) They can exhibit interference and diffraction

phenomena under suitable arrangements. Th~s, they may behave as waves.

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>

Positive Rays

Positive rays were discovered by Goldstein. Positive rays are moving positive ions of the gas filled in the discharge tube. The mass of these particles is nearly equal to the mass of the atoms of gas.

Properties of Positive Rays

(i) These consist of fast moving positively charged particles. (ii) These rays are deflected in magnetic field.

(iii) These rays are deflected in electric field. (iv) These rays travel in straight line.

. (v) Speed of positive rays is less than that of cathode rays. (vi) These rays can affect the photographic plate.

(vii) These rays penetrate through the thin aluminium foil. (viii) These rays can produce fluorescence and phosphorescence.

tt

> Photoelectric Effect

The phenomenon of ejection of electrons from a metal surface, when light of sufficient high frequency falls on it, is known as the photoelectric effect.

The figure given below shows the experimental set up to study photoelectric effect.

When ·a suitable radiation is incident on the

p

A ~---~+~v~---~

electrode P, electrons are ejer::ted from it. The electrons whi'cf.. 'ilave sufficient kinetic

en~~gy, ·~~ach'

_the

'e'lectr~de Q, ( de~pite its negative polarity).

,

The potential difference between the two electrodes acts as the retarding potential.

As electrons reach on electrode Q, so it becomes more and more negative, so fewer and fewer electrons reach on electrode Q and photo electric current recorded by ammeter falls. The particular potential difference V₀ (say) at which no electron reach on electrode Q, is called stopping potential. In this case; the work done by stopping potential is equal to the maximum kinetic energy of the electrons.

ie,

laws of Photoelectric Effect

Following are the laws of photoelectric effect

(i) For each emitting metal, there is a certain mirumum frequency v0 ( or maximum wavelength /..0 ) , called the threshold frequency of the incident radiation, below which no emission of photoelectron takes place, no matter how great is the intensity. The value of v₀ (or /..₀₎ is different for different emitting surfaces:

(ii) The process of emission of photoelectrons is an instantaneous process. There is no time lag ( <10-8 s) between the incidence of radiation and the emission of photoelectrons.

(iii) The maximum kinetic energy of the electrons emitted depends on the frequency of the incident light. It does not depend on the intensity of incident light.

(iv) The number of electrons emitted depends on the intensity of incident light and it does not depend on its frequency.

(v) The velocities (or the energies) of the emitted photoelectrons vary between zero · and a definite maximum Cvmax). The proportion of photoelectrons having a particular velocity is independent of the light intensity.

Explanation of laws of Photoelectric Effect

The photoelectric effect could not be explained by the wave theory of light which were later explained by Einstein's photon theory.

According to this theory, the energy of electromagnetic radiation is not continuously distributed over wavefront like the energy of water waves but remains concentrated in packets of energy content hv, where v is frequency of radiations and h is universal Planck's constant(= 6.625 x 10-34 _J-s).

Each packet of energy moves with the speed of light. The assumptions of Einstein's photon theory are

(i) The photoelectric effect is the result of collision of two particles, one of which is a photon of incident light and the other is an electron of photo-metal.

(ii) The electron of photo-metal is bound with the nucleus by Coulomb attractive forces. The minimum. energy required to free an electron from its bondage is called work function(~ = hv_{0 )}

(iii) The incident photon interacts with a single electron and loses its energy in two parts

(a) Firstly, in getting the electron released from the bondage of the nucleus.

(b) Secondly, to impart kinetic energy to emitted electron.

(iv) The efficiency of photoelectric effect is less than 1% ie, number of photons less than 1% are capable of ejecting

photoelectrons.

Thus, energy imparted by the photon = maximum kinetic

energy of the emitted electron

+

work function of the metal.

or _{hv =}1 2

2

mvmax +<I>

or _!mv2 _{= hv-"'}

2 max 'I'

... (i)

If the energy of the incident photcm is just equal to the work

function of the metallic surface, the kinetic energy of the metal

surface is zero.

Eq. (i) is referred as Einstein's photoelectric equation.

Substituting ~ = hv₀ in Eq. (i) 1 2

2

mvmax = hv- hv0 he he or A. A.0

Illustration 1 A metal has a work function of2.0 e V. It is illuminated by monochromatic light of wavelength 500 nm. Calculate (a) the

threshold wavelength, (b) the maximum energy of photoelectrons, (c) the stopping potential. (Given, Planck's constant, h

=

6.6 x 10-34 Js,

charge on electron, e = 1.6 x 10-19 _{C and 1 eV = 1.6 x 10-}19 _J).

Solution Here, h = 6.6 x 10-34 _{Js, e = 1.6 x 10-}19 _c, 1 eV = 1.6 X 10-19 J

~ = 2.0 eV = 2.0 X 1.6 X 10-19 = 3.2 X 10-19 J, A.= 500 run= 500x 10-9_m

(a) If A.₀ is the threshold wavel~ngth, then <1>= he

Ao

Ao

=he= 6.6xl0-34x3x108 <I> 3.2x 10-19 or = 618.75x 10-9_{m= 618.75 run}

(b) The maximum energy of the photoelectrons,

1 2 he -zmvmax = hv - <I>

=T-<1>

6.6x10-34x3xl08 _ 3.2x10_19 SOOxl0\9 = 3.96 X 10-19-3.2 X 10-19 = 0.76 X 10-19 J (c)"The stopping potential is given by

1 2 -19

eV₀=2mvmax =0.76xl0

or

v.

= 0.76xl0-19 = 0.76xl0-19 =0.475

v

0

e 1.6x10-19

Characteristics of Photoelectric Effect

(i) Effect of intensity Figure shows graph of photocurrent as a function of potential difference for light of constant frequency and two different intensities. When potential difference V is sufficiently large and positive, the current becomes constant. The stopping potential difference V₀ needed to reduce the current to zero is shown. For a given frequency if the intensity of light is increased (or we can say that number of photons incident per unit

area per unit time is increased) the.photoelectric current increases or viee-vers ; but the stopping potential remains the same.

Current (1)

Chapter

26

•

Electron and Photon

989

21

v =constant

--f.,--!:,---+Potential

0 difference (V)

(ii) Effect of frequency Figure shows the current as a

function of potential difference for two different frequencies

with the same intensity in each case.

Current (1)

(+)V

If the frequency is decreased, the stopping potenti&l

decreases and at a particular frequency of incident

light, the stopping potential becomes zero. This value

of frequency of incident light for which the stopping

potential is zero is called threshold frequency v_{0 •} If

the frequency of incident light (v) is less than the threshold frequency (v_0), no photoelectric emission

takes place.

(iii) Effect of photo-metal When frequency and intensity

of incident light are kept fixed and photo-metal is changed, we observe that stopping potential (V₅) versus frequency (v) graphs are parallel straight lines, cutting frequency axis at different

points. This shows that threshold frequency is different for different metals, the slope (:) for all the metals is same and

hence universal constant.

Metal1

' '

Figure shows that threshold freql,lency and workfunctiOJ.l are greater for metal 2 as compared to me tall.. ,

>(-10

Note

The negative potential applied to the

colfectci{

·

i~

~~d~r

1

to

'

~f;v;;;i

1

ffi~

-"

electrons reaching the collector (ie, to red'uce1he ~f,'cfto'~l~itric.'clirr~t\ftb'1 zero) is kirown as stop'ping·pOteOti'al. l ;r .. ~:-r~i,~'-P~ "1: ,;;r ... : {.1 '_)A:.X.'- :~, ~~ .• ~FL s

990

Chapter 26 • Electron ·and Photon

Important Features

Three major features of the photoelectric effect could not be explained by the wave theory of light which were later explained by Einstein's photon theory.

(a) Wave theory suggests that the kinetic energy of the photoelectrons should increase with the increase in intensity of light. However, Kmax = eV₀ suggests that it is independent of the intensity of light.

(b) According to wave theory, the photoelectric effect

should occur for any frequency of the light, provided that the light is intense enough. However, E ;::: <j> or

v 2:': v ₀ or A. $ /..

0 suggest that photo mission is possible

only when frequency of incident light is either greater than or equal to the threshold frequency ,.0 .

• The electrons will be emitted from metal surface only if the frequency of incident light is greater than threshold frequency v_0.

• The el;ct~c>ns are emitted instantaneously. The interaction between

photons and electrons is one to one. So, weak incident light very few photons arrive per unit time, but each one has enough energy to eject an electron instantaneously.

• The work . .fu~ction ~ and threshold frequency \'o varies from metal to metal.

• The frequency\' and wavelength A, are related as ,.

=

c/'A..The energy of photon

=

hv

=

he

A,'

• For a given intensity I

=

nhv greater the frequency lesser will be number of photons. Hence, lesser will be photoelectric current ie, p_hotocurrent

0<.!.0<

A.. v

Instance 1 Photoelectric threshold of silver is A.

=

3800

A.

Ultraviolet light of A. = 2600

A

is incident on silver surface. What will be the value of work function? .

(a) 5.23 x

w-

19 J (b) 6.5 x

w-

18 J (c) 6.5 x

w-

19 J (d) 5.5 x

w-

10 J Interpret Here A.₀

=

3800

A

Work function

~

0

or W = hv ₀ =

~

A.o 6.63 X 10-34 X 3 X 108 3800x 10-10 = 5.23 x 10-19 J (3.2 eV)

Instance 2 In the above instance, what will be the maximum kinetic energy of the emitted photoelectrons?

Car 2.5 eV (b) 1 eV

(c) 1.51 eV (d) 3.51 eV

Interpret Incident wavelength A.

=

2600

A

. . d ·~ fr c 3x108 :. ,. = mc1 ent equency = - = Hz A 2600 X 10-10 Then KEmax = hv - <Jb 6.63 X 10-34 X 3 X 108 hv= 10 =7.6Sx10-19 J=4.78eV

2600x10-KEmax = hv

-%

= 4.78eV- 3.27 eV = 1.51eV (2.42X 10-19 J)

Instance 3 In the above instance; what will be the maximum velocity of the photoelectrons? (Mass of the electron= 9.11 x

w-

31 kg}

(a) .1 m x, 6 ms-1 _{•. . (b). 1.5 ms-}1 _{.· · ,} (c) 0.7289 x 106 ms-1 (d) q,56 x 10~.m.s,-1. .. .

Interpret KEmax =

~mv~a

x

V =

~2KEm

ax

=

max

m

2 X 2.42 X 10-19

9.llx1o-31

=

0.7289 x 106 _ms-1

~

~

Planck's Quantum Theory

When a black body is heated, it emits thermal radiations of

different wavelengths or frequency. To explain these relations,

Max Planck put forward a theory known as Planck's quantum

theory. The main points of quantum theory are

(i) Substance radiate or absorb energy discontinuosly in

the form of small packets or bundles of energy.

(ii) The smallest packets of energy is called quantum. In

case of light the quantum is known as photon.

(iii) The energy of a quantum is directly proportional to the

frequency of the radiation. E oc v (orE = hv =

~)

where v is the frequency of radiation and h(6.626 x 10-34 J-s) is Planck's constant and

c (3 x 108 ms-1_{) is velocity of light} hv h Momentum of photon p = - = -Rest mass of photon

=

0 c A.

D ynarruc or net1c mass o p oton. k i . f h , m

= - = -

hv h

c2 cA.

(iv) A body can radiate or absorb energy in whole number multiples of a quantum hv, 2hv, 3hv ... nhv where n is

the positive integer.

w

~

Compton Effect

When a monochromatic beam of X-falls on a target containing

free electrons, it is scattered. As a result, the electrons recoil and

the scattered radiation has wavelength longer than incident one.

This effect is called Compton effect.

(i) A.' - A.

=

D.A.

=

Compton shift

h

D./..= - [ 1 -cos <j>]

m0c

where m0 is rest mass

Incident of an electron and

c is the speed of light

hjm

0c = Compton shift X-ray photon D.A is maxinlum when (wavelength ) ~ = 180° .

(ii) Kinetic energy of recoil electron

he he

Ek =T-~

(iii) Direction of recoil electron tan El = /..sin <I>

A.'-: /..cos <j> (iv) Compton wavelength of electron

h 0

=-=0.024A mbc

(v) Maximum Compton shift

2h 0 (D./..)max = -':" 0.048 A m₀c Scattered X-rays Carbon target

Chapter 26

•

Electron and Photon

991

llltext Questions

26.1

(i) Db Xcrays show phenomenon of photoelectric effect?

(ii) It is harder to remoy~ a free electron frgm copper than from sodium? Which metal has greater work function? Which has higher

tpre§hg~d vyavel~llgt~?

G;re!j~ ~p~~> ejEcts electrons ~m

a

Srrtain photosensitive surface, yellow light does not. Will (a) red light (a) violet light eject ~~o~ge~sc~~ from the same substance ?

(iv) A photon and an electron have same wavelength. Which particle is moving faster?

~

>

Dual Character of Radiation

In case of light some phenomenon like diffraction and interference can be explained on the basis of its wave character. However, the certain other phenomenon such as black body radiation and photoelectric effect can be explained only on the basis of its particle nature. Thus light is said to have a dual character. Such studies on light wave were made by Einstein in 1905. Louis-de-Broglie, in 1942 extended the idea of photons to material particles such as electron and he proposed that matter also has a dual character as wave and as particles.

De-Broglie Relation

According to de-Broglie a wave is associated with energy moving particle. These waves are called de-Broglie waves or matter waves.

According to quantum theory, energy of photon

E = h ... (i)

If mass of the photon is taken as m, then as per Einstein's equation

E = mc2 ••• (ii)

From Eqs. (i) and (ii) h\' = mc2

h ~ = mc2

, where A. = wavelength of photon.

A. h

A.

=--me

de-Broglie asserted that the above equation is completely a general function and applies to photon as well as all other moving particles.

A

-!!__

= h

-So,

- mv .J2mE

where m is mass of particle and v is its velocity.

(i)-de-Broglie wavelength associated with charged particle A-~-_h__ h

- p - .JzmE - ~2mqV

(ii) de-Broglie wavelength of a gas molecule

A

= __

h_ where T absolute temperature

.J3mkT

k = Boltzmann's constant

=

1.38 x 10-23 J/K

(iii) Ratio of wavelength of photon and electron. The ) wavelength of photon of energy E is given by A = he

P

E

'while the wavelength of an electron of kinetic energy K is given by A. =

b .

Therefore for same energy, the

c

-v2mK

ratio

AP

=

.:._.JzmK

=

~2mc

2

K

, Ae E . E2

Instance 4 Calculate the de-Broglie wavelength of neutrons whose energy is 1 eV (Given mass of electrons= 1.67 x 10-27 kg)

Interpret We know that

h A= .J2mE 6.6x 10-34

~2

X 1.67 X 10-27 X 1.6 X

10~

19 = 0.2857 X 10-lQ

=

0.2857

A.

Davisson and Germer Experiment

The wave nature of the material particles as predicted by de-Broglie was confirmed by Davisson and Genner (1927) in United States and by G P Thomson (1928) in Scotland.

Experimental arrangement used by Davisson and Germer is as shown in figure. Electrons from hot tungsten cathode (C) are accelerated by a potential difference V between the cathode and anode (A). A narrow hole in the anode renders the electrons into a fine beam of electrons and allows it to strike the nickel crystal. The electrons are scattered in all directions by the atoms in the crystal. The intensity of the electron beam scattered in a given direction is found by the use of a detector. By rotating the detector about an axis through the point 0, the intensity of the scattered beam can be measured for different values of~. the angle between incident and the scattered direction of electron beam.

OJ CD w 3 A Electron gun ·· .. Detector

Davisson and Germer, found that the intensity of scattered beam of electrons was not the same but different at different angles of scattering. It is maximum for diffracting angle' 60° at 54 volt potential difference.

992

Chapter 26

•

Electron and Photon

54V

If the de-Broglie waves exist· for electrons then these should be diffracted as X-rays. Using the Bragg's formula 2d sine = n A, we can determine the wavelength of these waves. Where d = distance between diffracting planes

e

=

(ISO-<I>)

=

glancing angle for incident beam= Bragg's angle. 2 The distance between diffracting planes in Ni-crystal for this experiment is d = 0.91

A

and the Bragg's angle = 65°. This gives for n = 1, A = 2 x 0.91 x 10-lo sin 65° = 1.65

(9

,,

9}0 . 0 ... ..,:.___,_ _ _ _ _ _ _ _

\:~~.Yd··

....

···..,~tori1i.c planes the

Now de-Broglie wavelength can also be determined by using

C l 1 _ 12.27 _ 12.27 _ 1 67Ao

!OrillU a "-

rv

-

.JS4 --

0 0 Thus the de-Broglie hypothesis is verified.

lntext Questions

26.2

,

tic energy; which of the following has smallest de-Broglie }Vavelength, electron, proton, a-particle?

''nature of lnatter not apparent to our daily observations ? ....

wavelength pf a photon of an electromagnetic radiation

elnl.~ltothewaV'elength

of the radiatip:;?> ,, . '> .

,

Chapter 26

•

Electron and Photon

993

kinetic energy with which an "'""''-w.vu

einitted from a metal surface is independent of the f the light and depends upon its frequency.

The number of photoelectrons emitted ,is mctep,en,aeJlt the frequency of th · cident llght

· its intensity.

: Einstem's equation of photoelectric effect.

1 2

2mvmax

1 2 2mvrriax

bove relation is veH~n?;Inof the wave ve1enl'lll of particle. 16. de-Broglie wavelength of

llluSlrative

Example 1 What is frequency and energy of a photon of wavelength

6000

A?

(Given h = 6.6 x 10-34 Js, c = 3 x 108 _ms-1)

(a) 15 x 104_{Hz and 3.3x 1o-}10_J

(b) 6 x 1010Hz and 4.4X 10-19 _J (c) 5 x 1012_{Hz and 3.3 x 10-}19 _J (d) 5 x 1014Hz and 3.3 x 10-19 J . e 3x 108 SolutiOn Frequency v =-;;- = ₁₀ = 5 x 1014 Hz 11, 6000xl0-and energy= hv = 6.6 x 10-34 x 5 x 1014 = 3.3 x 10-19 _J Example 2 The work function of sodium is 2.3 eV. Calculate the

maximum wavelength for the light that will cause photoelectrons to be emitted from the sodium.

(aJ 64oo

A

(bJ 5ooo

A

(c) 54oo

A

(d) 5200

A

Solution KEmax

=

hv - <1b

=

he -q> 0 A. he

T-

q>₀ > 0 (Kin~tic energy is always +ve) A-<.0._

q>o

A. = eh = 3x108 x6.62x10-34 =

5400

A

max q>₀ 2.3 X 1.6 X 10-19

Example

3

In an experiment on photoelectric effect it was observed that for incident light of wavelength 1. 98 X 10-7 m, stopping potential

is 2.5 V. Wh~t is the energy of photoelectrons with maximum speed,

workfunction ~₀ and threshold frequency?

(a) 6.25 eV, 3.75 eV, 9.10 x 1014 Hz

(b) 3.75eV, 6.25 eV, 9.10x1014 Hz

(c) 4.75 eV, 6.25 eV,8.10x1014 Hz

(d) None of the above

Solution

I<Emax

= eV = 2.5 eV

Energy of the incident light

E =he= 6.6x10-34 x3x108

A. 1.98 x 10-7

6.6 X 10-34 X 3 X 108 eV = 6.25 eV

1.98x1o-7 _x1.6x1o-19 Now, work function

C~o) =E-KE =3.75 eV Moreover ~o

=

hvo • <i>o Yo=h 3.75xl.6x1o-I9 =9.10x1014Hz Yo 6.6x10-34

,

Example 4 Find the ratio of de-Broglie wavelength of proton and a-partide which has been accelerated through the same potential difference.

(a)

3J2

(c)

2.)3

(b) 2J2

(d)

zJS

Solution A.- h AP _ 2maqa.V

- ~2mqV 'A.a. - 2mPqP V

As mP =_!_and qa =

3_

ma 4 qp 1

!J__

= )4 X 2 =2J2

A

a.

Example 5 The anode voltage of a photocell is kept fixed. The wavelength A. of the light falling on the cathode is gradually changed.

The plate current i of the photocell varies as follows.

(~·~

(b)~~

(c)

l_l

(d)

lL

A. A.

Solution On increasing wavelength of light the photoelectric current decreases and at a certain wavelength (cut-off) above which photoelectric current stops. Hence graph (a) is correct.

Example 6 The ratio of de-Broglie wavelengths of molecules of hydrogen and helium which are at temperature 27°C and 12TC

respectively is (a) 1 2 (c)

JI

Solution (b)

)!

(d) 1 h Wavelength A. = - -mvrms 4(273 + 127) 2(273 + 27)

Chapter Practice

Exercise I

Cathode and Positive Rays

1. Doubly ionised helium atom and hydrogen ions are accelerated, from rest, through the same potential

difference. The ratio of final velocities of helium and

hydrogen is

(a) 1 : ../2

(c) 1 : 2

(b)../2:1

(d) 2 : 1

2. In Thomson's mass spectrographs, when an electric field

of 2 X 104 _Vm-1 _{is applied then the deflection produced} on the screen is 20 mm. If the length of the plates is 5 em

and the distance of the screen from plates is 21 em and

the velocity of positive ions is 106 ms-1, then their specific

charge will be

(a) 107 Ckg-1

(c) 5.9 X 107 _Ckg-1

(b) 2.59 X 107 Ckg-1 (d) 9.52 X 107 _Ckg-l 3. The working principle ~f the mass spectrograph is that

for a given combination of accelerating potential and

magnetic field, the ion beam (with charge q and mass M)

to be collected at different positions of ion collectors will

depend upon the value of (a) ~q/ M

(c) q/M

(b) (q/M)2

(d) qM

4. The mass of a proton is 1836 times that of an electron.

An electron and a proton are projected into a uniform

electric field in a direction perpendicular to the field with

equal initial kinetic energies. Then

(a) the electron trajectory is less curved than the proton

trajectory

(b) the proton trajectory is less curved than the electron

trajectory

(c) Both trajectories are equally curved

(d) Both trajectories will be straight

5. An ionisation chamber, with parallel conducting plates as

anode and cathodes has 5 x 107 cm-3 electrons and the

same number of singly charged positive ions per cm3. The

electrons are moving toward the ar:ode with velocity 0.4 ms-1. The current density from anode to cathode is 4J,!Am-2.

The velocity of positive ions moving towards cathode is

(a) 0.1 ms-1 _{(b) 0.4 ms-}1

(c) zero (d) 1.6 ms-1

6. In Thomson mass spectrograph, singly and doubly ionised

particles from similar parabola corresponding to magnetic

fields of 0.8 T and 1.2 T for a constant electric field. The

ratio of

,

masses of ionised particles will be

(a) 3 : 8 (c) 8 : 3

(b) 2: 9 (d) 9 : 2

7. In an ionisation experiment it is found that a doubly ionised particle enters a magnetic field of 1 T and moves in a circular path of radius 1 m with a speed of

1.6 x 107 ms-1. The particle must be

(a) c++ (b) Be++

(c) Li++ (d) He++

8. An a-particle of mass 6.65 x 10-27 kg travels at right angles to a magnetic field of 0.2 T with a speed of

6 x 105 ms-1. The acceleration of a-particle will be

(a) 5.77 x 1011 ms-2 (b) 7.55 x 1011 ms-2

(c) 5.77x 1012 _ms-2 _{(d) 7.55 x 10}12 _ms-2

9. Cathode rays of velocity 106 ms-1 describe an

approximate circular path of radius 1 m in an electric

field of 500 V cm-1. If the velocity of cathode rays is

doubled, the value of electric field needed so that the rays describe the same circular path is

(a) 1000 V cm-1 (b) 1500 V cm-1

(c) 2000 V cm-1 (d) 500 V cm-1

10. An oil drop with charge q is held stationary between two.

plates with an external potential difference of 400 V. If

the size of the drop is doubled without any change of charge, the potential difference required to keep the drop stationary will be

(a) 400 V (c) 3200 V

(b) 1600

v

(d) 4000

v

11. Air becomes conducting when the pressure ranges

between

(a) 76 em and 10 em (b) 10 em and 1 em

(c) 1 em and 10-3 _{em (d) 10--4 em and 10-}7 _em

12. An electron of mass m and charge q is accelerated from

rest in a uniform electric field of strength E. The velocity

acquired by it as it travels a distance l is

(a) ~2Eql!m

(b) ~2Eq!ml

(c) ~2Em! ql

(d) ~Eq!ml

13. A proton of mass 1.67 x 10-27 kg enters a uniform

magnetic field of 1 Tat point A as shown in figure, with a

speed of 107 ms-1. The magnetic field is directed normal

to the plane of paper downwards. The proton emerges

out of the magnetic field at point C, then the distance AC

996

Chapter 26 • Electron and Photon

X X X X 45° ---7 B X X X X A X X X X

c

X X X X X X X X (a) 0.7 m, 45° (b) 0.7 m, 90° (c) 0.14 m, 90° (d)· 0.14 m, 45°

14. An oil drop of mass 50 mg and of charge -5 J.!C is just balanced

in air against the force of gravity. Calculate the strength of the electric field required to balance is, (g = 9.8 rns-2)

(a) 98 Nc-1 upwards (b) 98 Nc-1 _downwards

(c) 9.8 Nc-1 towards north (d) 9.8 Nc-1 towards south

15. A charged particle is moving in the presence of electric

~ ~ ----t --7

field E and magnetic field B. The directions of E and B

are such that the charged particle moves in a straight line --> -->

and its speed increases. The relations amongst E , B and -->

velocity v must be such that -->--> --> (a) E · B = 0, v is arbitrary (b) (c) (d) -->--> -->

E, B and v are all parallel to each other.

--7 ---? --t --7 ---? ---?

E · v = 0; B · v = 0 but E · B ,t 0

--> --> -->

v is parallel to E and perpendicular to B

16. An electron with (rest ma:;s m_{0 )} moves with a speed of 0.8 c. Its mass when it moves with this speed is

(a) m0 (b) m0 /6

(c) 5m0/3 (d) 3m0/5

17. A charged dust particle of radius 5 x 10-7 m is located in a horizontal electric field having an intensity of 6.28 x 105 vm-1. The surrounding medium in air with coefficient of viscosity 11

=

1.6 x 10-15 Nsm-2. Ifthis particle

moves with a uniform horizontal speed of 0.01 ms-1, the number of electrons on it will be

(a) 20 (b) 15

(c) 25 (d) 30

18. The momentum of a charged particle moving in a perpendicular magnetic field depends on

(a) its charge

(b) the strength of magnetic field (c) radius of its path

(d) All of the above

19. If in a Thomson's mass spectrograph, the ratio of the electric fields and magnetic fields, in order to obtain coincident parabola of singly ionised and doubly ionised positive ions are 1 : 2 and 3 : 2 respectively, then the ratio of masses of particles will be

(a) 3 : 1 (b) 2 : 1

(c) 9 : 4 (d) 9 : 2

20. The specific charge for positive rays is much less than that for cathode rays. This is because

(a) masses of positive rays are much larger

(b) charge on positive ray is less (c) pGJsitive rays are positively charged (d) experimental method is wrong

21. If a cathode ray tube has a potential difference V volt between the cathode and anode, then the speed v of cathode rays is given by

(a) v oc V2 (b) v oc

JV

(c) v oc

v-

1 (d) v ~

v

22. An electric field of intensity 6 X 104 _{Vm-l is applied} perpendicular to the direction of motion of the electron.

A magnetic field of induction 8

x

10-2 wm-2 is applied perpendicular to both the electric field and direction of motion of the electron. What is the velocity of the electron if it passes undeflected?

(a) 7.5 x 105 ms-1 (c) 48 X 10-2 ms-1

(b) 7.5 x 10-5 _ms-1

(d) It is never possible 23. The mean free path of the electrons in a discharge tube is

20 em. The length of the tube is 15 em only. Then length of Crooke's dark space is

(a) 5 em (b) 20 em (c) 15 em (d) 2S em

24. The mass of a particle is 400 times than that of an electron and charge is double. The particle is acce'lerated by SV.

Initially the particle remained in rest, then its final kinetic energy will be

(a) 5 eV · (b) 10 eV (c) 100 eV (d) 200 eV

25. A charged particle is moving in a uniform magnetic field in a circular path. The energy of the particle is tripled. If the initial radius of the circular path was R,

the radius of the new circular path after the energy is tripled will be

(a)

~

(b) ../3R

3

(c)

3

R (d) R/ ../3

26. An electron moving with a variable linear velocity v in a variable magnetic field B will remain rotating in a circle of constant radius r only when

(a) B is held constant (b) vis held constant (c) Both v and Bare constant (d) None ofthe above

27. elm ratio of anode rays produced in a discharge tube,

depends on the

(a) nature of the gas filled in the tube (b) nature of the material of anode (c) nature of the material of cathode (d) All of the above

28. A positively charged particle enters a magnetic field of value

BJ

with a velocity vk. The particle will move along

(a) +X axis (c)

+

Z axis

(b) -X axis (d) -Z axis

29. In a mass spectrograph, an ion X of mass number 24 and charge +e and another ion Y o[ mass number 22 and charge

+

2 e enter in a perpendicular magnetic field with the same velocity. The ratio of the radii of the circular path in the field will be

(a) 11/22 (b) 11/2

30. A beam of electrons of velocity 3 x 107 ms-1 is deflected

1.5 mm is passing 10 em through an electric field of

1800 vm-1 perpendicular to their path. The value of elm for electron is

(a) 1.78 x 1011 C kg-1

(c) 1.5 X 1011 Ckg-1

Particle Nature

'

ofLight

(b) 2 X 1011 Ckg-1 (d) 3.5 X 1011 Ckg-1

31. Planck's constant has the dimensions of

(a) energy (b) mass

(c) frequency (d) angular momentum

32. The wavelength of a 1 keV photon is 1.24 x 10-9 m. What is the frequency of 1 MeV photon?

(a) 2.4 X 1015 Hz (b) 2.4 X 1020Hz

(c) 1.24 x 1015 Hz (d) 1.24 x 1020 Hz

33. A parallel beam of light is incident normally on a plane surface absorbing 40% of the light and reflecting the rest. If the incident beam carries 60 W of power, the force

exerted by it on the surface is

(a) 3.2 X 10-8 N (b) 3.2 X 10-7 N

(c) 5.12 X 10-7 N (d) 5.12 X 10-8 N

34. Calculate the energy of a photon with momentum 3.3 x 10-13 kg-ms-1, given Planck's constant to be 6.6 x 10-34 Js (a) 7.3 x 104 J (c) 1.3 x 105 J 35. Momentum of a wavelength is (a) hi/P (c) ph (b) 9.9 X 10-5 J (d) 8.1 X 103 J

photon is p. The corresponding

(b) plh

• (d) hlp

36. Which of the following statement about photon 1s incorrect?

(a) Photons exert no pressure (b) Momentum of photon is h\'lc

(c) Photon's rest mass is zero (d) Photon's energy ish\'

37. A photon in motion has a mass equal to (a) clh\' (b) hi'A

(c} h\' (d) hvlc2

38. Momentum of a photon of wavelength A. is (a) hi'A (b) h A;c2

(c) hAle (d) zero

39. A photon will have less energy, if its

(a) amplitude is higher (b) frequency is higher

(c) wavelength is longer (d) wavelength is shorter 40. An important spectral emission line has a wavelength

of 21 em. The corresponding photon energy is

( h= 6.62 x 10-34 Js and c = 3 x 108 ms-1) (a) 5.9 X 10-8 eV (b) 5.9 X 10-4 eV (c) 5.9 X 10-6 eV (d) 11.8 X 10-6 eV

41. The energy of a photon of green light of wavelength

50000 A is

(a) 3.459 X 10-19 J (b) 3.973 X 10-19 J

(c) 4.132 X 10-19 J (d) 8453 X 10-19 J

42. What will be the number of photons emitted per second by a 10 W sodium vapour lamp assuming that 90% of the

consumed energy is convei,ted into light? Wavelength of sodium light is 590 nm, h = 6.63 x 10-34J-s.

Chapter 26

•

Electron and Photon

997

(a) 0.267 x 1018 (c) 0.267 x 1020

(b) 0.267 X 1019 (d) 0.267 X 1017

43. If the energy of photons corresponding to the wavelength

of 6000A is 3.2 x 10-19 J, the photon energy for a

wavelength of 4000 A will be

(a) 1.11 X 10-19 J (b) 2.22 X 10-19 J

(c) 4.40 x 10-19 J (d) 4.80 x 1o-19 J

44. A radio transmitter operates at a frequency 880 kHz and a power of 10 kW. The number of P;hotons emitted per

second is 1

(a) 1.72 X 1031 (b) 1.327 X 1025 (c) 1.327 x1o37 (d) 1.327 x1o45

Emission of Electrons and Photoelectric Effect

45. The photoelectric threshold of Tungsten is 2300 A. The

energy of the electrons ejected from the surface by

ultraviolet light of wavelength 1800 A is (h = 6.6

x

10-34 J-s)

(a) 0.15 eV (c) 15 eV

(b) 1.5 eV

(d) 150 eV

46. A light of wavelength 4000 A iS" allowed to fall on a metal

surface having work function 2 eV. The maximum velocity

of the emitted electrons is (R = 6.6 x 10-34Js)

(a) 1.35 X 105 ms-1 (b) 2.7 X 105 ms-1 (c) 6.2 x 105 ms-1 (d) 8.1 x 105ms-1

47. Ultraviolet radiation of 6.2eV falls on an aluminium

surface (work function 4.2eV). The kinetic energy in joule

of the fastest electron emitted is approximately (a) 3 X 10-21 (b) 3.2 X 10-19

(c) 3 X 10-17 (d) 3 X 10-15

48. Radiations of two photon's energy, twice and ten times

the work function of metal are incident on the metal surface successively. The ratio of maximum velocites of

photoelectrons emitted in two cases is (a) 1 : 2 (b) 1 : 3

(c) 1 : 4 (d) 1 : 1

49. The variation of photoelectric current given by the

photocell, with the intensity of light, is given by a graph, which is a straight line with

(a) +ve slope with intercept on current axis

(b) -ve slope with intercept of current axis

(c) +ve slope passing through origin (d) -ve slope passing through origin

50. When the photons of energy hv fall on a photosensitive

metallic surface (work function h\'0 ) electrons are emitted

from the metallic surface. The electrons coming out of

the surface have some kinetic energy. The most energetic

ones have the kinetic energy equal to

(a) less (c) equal

Vs

A B

(b) more

I

998

Chapter 26

•

Electron and Photon

51. When the photons of energy hv fall on a photosensitive

metallic surface (work function h\'0 ), electrons are

emitted from the metallic surface. The electrons coming

out of the surface have some kinetic energy. The most

energetic ones have the kinetic energy equal to

(a) hv₀ (b) h

(c) h -hv₀ (d) hv

+

h'·o

52. For a certain metal ,. = 2 v0 and the electrons come out

with a maximum velocity of 4 x 106 ms-1. If the value of

v = 5 v_{0 ,} then maximum velocity of photoelectrons will be

(a) 2 x 107 _ms-1 _{(b) 8 x 10}6 _ms-1

(c) 2 x 106 _ms-1 _{(d) 8 x 10}5 _ms-1

53. The wavelength of the photoelectric threshold for silver is !.._{0 .} The energy of the electron ejected from the surface of

silver by an incident light of wavelength A(A < A0 ) will

be

(a) hc(A_{0 -} A)

(c)

!!._(.!_ _

_!___]

c A A₀

54. A metal surface is illuminated by a lig4t of given intensity

and frequency to cause photoemission. If the intensity

of illumination is reduced to one-fourth of its original

value, then the maximum kinetic energy of the emitted

photoelectrons would become (a) four times the original value (b) twice the original value

(c) l/6th of the original valu~ (d) unchanged

55. The work function of a metal is leV. Light of wavelength

3000

A.

is incident on this metal surface. The velocity of

emitted photoelectons will be

(a) 10 ms-1 _{(b) 10}3 _ms-1

(c) 104 ms-1 (d) 106 ms-1

56. In the photoelectric effect the velocity of ejected electrons

depends upon the nature of the target and . (a) the ~equency of the incident light

(b) the polarisation of the incident light

(c) the time for which the light has been incident (d) the intensity of the incident light

57. Light of wavelength 4000

A.

is incident on a metal plate

whose work function is 2 eV. The maximum KE of the

emitted photoelectron would be (a) 0.5 eV (b) 1.1 eV

(c) 1.5 eV (d) 2.0 eV

58. A photon of energy 3.4 eV is incident on a metal having work function 2 eV. The maximum KE of photoelectrons is equal to

(a) 1.4 eV (c) 5.4 eV

(b) 1.7 eV (d) 6.8 eV

59. The frequency of the incident light falling on a

photosensitive metal plate is doubled, the kinetic energy

of the emitted photoelectron is (a) double the earlier value (b) unchanged

(c) more than doubled (d) less tham doubled

60. A metal surface of work function 1.07 eV is irradiated with light of wavelength 332 nm. The retarding potential required to stop the escape of photoelectrons is

(a) 1.07 eV (b) 2.66 eV

(c) 3.7 eV (d) 4.81 eV

61. If the work function for a certain metal is 3.2 x 10-19 J and it is illuminated with light of frequency v

=

8 x 1014 Hz, the maximum kinetic energy of the photoelectron would be

(a) 2.1 X 10-19 _{J (b) 3.2 X 10-19 J}

(c) 5.3 x lo-19 _{J (d) 8.5 x 10-19 J}

62. Ultraviolet radiations of 6.2 eV falls on an aluminium surface. KE of fastest electron emitted is (work function

=

4.2 eV)

(a) 3.2 x 10-21 J

(c) 7 x 10-25 J

(b) 3.2 X 10-19 J

(d) 9

x

lo-32 J

63. Ultraviolet light of wavelength 300 nm and intensity 1.0 wm-2 falls on the surface of a photosensitive material. If one percent of the incident photons produce photoelectrons, then the number of photoelectrons emitted from an area of 1.0 cm2 of the surface is nearly (a) 9.61 x 1014 s-1 (b) 4.12 x 1013 _s-1

(c) 1.51x 1012s-1 _{(d) 2.13x 10}11_s-1

64. The photoelectric threshold wavelength for a metal surface is 6600

A..

The work function for this metal is

(a) 0.87 eV (b) 1.87 eV

(c) 18.7 eV (d) 0.18 eV

65. Light of wavelength 4000

A.

incident on a sodium surface for w~ich the threshold wavelength of photoelectrons is 5420 A. The work function of sodium is

(a) 0.57 eV (b) 1.14 eV

(c) 2.29 eV (d) 4.58 eV

66. The difference between kinetic energies of photoelectrons emitted from a surface by light of wavelengths 2500

A.

and 5000

A.

will be

(a) 1.61 eV (b) 2.47 eV

(c) 3.96 eV (d) 3.96 x 1o-19 eV

67. When a point source oflight is 1 m away from~ photoelectric cell, the photoelectric current is found to be I rnA. If the same source is placed at 4 m from the same photoelectric cells, the photoelectric current (in rnA) will be

(a) l/16 (b) l/4

(c) 41 (d) 161

Wave Nature

ofParticle

68. An electron and photon have same wavelength. If E is the energy of photon and p is the momentum of electron, then the magnitude of E/p in SI unit is

(a) 3.33 x 10-9 _{(b) 3.0 x 10}8

(c) 1.1 X 10-19 (d) 9 X 1016

69. The wavelength of de-Broglie wave associated with a thermal neutron of mass m at absolute temperature T is

given by (Here, k is the Boltzmann constant)

h h

(a)

~2mkT

(b)

~mkT

(c) h

70. The de-Broglie wavelength of a neutron at 927°C is A.

What will be its wavelength at 27°C?

(a) A./2 (b) A./4

(c) 4 A (d) 2 A

71. What should be the velocity of an electron so that its momentum becomes equal to that of a photon of

wavelength 5200

A?

(a) 700 ms-1 _{(b) 1000 ms-}1

(c) 1400 ms-1 _{(d) 2800 ms-}1

·

n.

If the mass of neutral 1.7 x 10-27 kg, then the

de-Broglie wavelength of neutral of energy 3eV is (h = 6.6 x 10-34 J-s)

(a) 1.6 x 10-16 m

(c) 1.4 x 10-10 m

(b) 1.6 x 10-11 m

(d) 1.4 x 10-11 m

73. A particle with rest mass m₀ is moving with speed of light

c. The de-Broglie wavelength associated with it will be

(a) infinite (b) zero

(c) m0clh (d) hvlm0 c

74. An electron of mass m and charge e initially at rest gets

accelerated by a constant electric field E. The rate of

change of de-Broglie wavelength of this electron at time t ignoring relativistic effects is

-h

(a) eEt2 -mh (c) eEt2 -eEt (b) E (d) -h eE

75. What should be the velocity of an electron so that its momentum becomes f'!qual to that of a photon of

wavelength 5200

A?

Chapter 26

•

Electron and Photon

999

(a) 103 ms-1 (c) 1.4 x 103 ms-1

Principle of Uncertainty

(b) 1.2 x 103 ms-1

(d) 2.8 x 103 ms-1

76. The correctness of velocity of an electron moving with velocity 50 ms-1 is 0.005%. The accuracy with which its position can be measured will be

(a) 4634

x

10-3m (b) 4634

x

10-5m (c) 4634 x 10-6m (d) 4634 x 10-8m

77. If a proton and an electron are confined to the same region, then uncertaint'y in momentum

(a) for proton is more, as compared to the electron (b) for electron is more, as compared to the proton

(c) same for both the particles

(d) directly proportional to their masses

78. If the uncertainty in the position of an electron is 10-10 m, then the value of uncertainty in its momentum (in kg-ms-1_{) will be}

(a) 3.33 X 10-24 (b) 1.03 X 10-24 (c) 6.6 X 10-24 _{(d) 6.6 X 10-24}

79. The uncertainty in the position of a particle is equal to the

de-Broglie wavelength. The uncertainty in its momentum will be

(a) lilA (b) 2hi3A.

(c) 'Alii (d) 3A/2h

80. If the uncertainty in the position of proton is 6

x

108 m, then tl1e minimum uncertainty in its speed will be (a) 1 cms-1 _{(b) 1 ms-}1

(c) 1 mms-1 (d) 100 ms-1

Exercise II

Only One Correct Option

1. When radiation is incident on a photoelectron emitter,

the stopping potential is found to be 9 V. If elm for the electron is 1.8

x

1011 Ckg-1, the maximum velocity of

ejected electrons is

(a) 6 x 105 ms-1

(b) 8 x 105 ms-1

(c) 106 ms-1

(d) 1.8 x 106 ms-1

2. The intensity of X-rays from a coolidge tube is plcitted against wavelength A as shown in figure. The minimum

wavelength found is

"-

c

and the wavelength of Ka like is

"-K·

As the accelerating voltage is increased

(a) A.K-Ac increases

(c) A.J! increases

(b)· A.K-

"-c

decreases

(d) A.K decreases

3. The stopping potential V for photoelectric emission for a metal surface is plotted along Y-axis and frequency v of incident light along X-axis. A straight line is obtained as shown. Planck's constant is given by

(a) slope of the line

(b) product of slope of the line and charge on the electron (c) intercept along Y-axis divided by charge on the electron (d) product of intercept along X-axis and mass of the

electron

(e) product of slope and mass of the electron

4. Mixed He+ and 02+ ions (mass of He+ = 4 amu and that of

o

2_{+= 16 amu) beam passes a region of constant}

perpendicular magnetic field. If kinetic energy of all the ions is same then

(a) He+ ions will be deflected more than those of

o

2₊

(b) He+ ions will be deflected less than that of

o

2+ (c) all the ions will be deflected equally

(d) no ions will be deflected

5. In Millikan's oil drop experiment a drop of charge Q and radius

r

is kept constant between two plates of potential difference of 800 V. Then charge on other drop of radius 2 r which is kept constant with a potential difference of 3200 Vis

(a) Q 12 (c) 4 Q

(b) 2 Q

1000

Chapter

26

•

Electron and Photon

6. An electron and a proton have the same de-Broglie

wavelength. Then the kinetic energy of the electron is (a) zero

(b) Infinity

(c) equal to kinetic energy of the proton

(d) greater than the kinetic energy of proton

7. Energy required to remove an electron from an aluminium surface is 4.2 eV. If light of wavelength 2000

A

falls on the surface, the velocity of fastest electrons ejected from the

surface is

(a) 2.5 X 1018 ms-1

(c) 6. 7 x 1018 ms-1

(b)

2.5

x 1013 ms-1

(d) None of these

8. The maximum wavelength of radiation that can produce

photoelectric effect in certain metal is 200 run. The maximum kinetic energy acquired by electron due to

radiation of wavelength 100 run will be

(a) 12.4 eV (b) 6.2 eV

(c) 100 eV (d) 200 eV

9. Consider the following statements concerning electrons :

I. Electrons are universal constituents of matter.

II. J J Thomson received the very first Nobel prize in Physics for discovering the electron.

III. The mass of the electron is about 1/2000 of a

neutron.

IV. According to Bohr the linear momentum of the electron is quantised in the hydrogen atom. Which of the above statements are not correct?

(a) I (b) II

(c) III (d) IV

10. Electron with energy 80 keV are incident on the tungsten target of an X-ray tube. K shell electrons of tungsten have

-72.5 keV energy. X-rays emitted by the tube contain only

(a) a continuous X-ray spectrum (Bremsstrahlung) with a minimum wavelength of- 0.155 A

(b) a continuous X-ray spectrum (Bremsstrahlung) with

all wavelengths

(c) the characteristic X-ray spectrum of tungsten

(d) a continuous X-rays spectrum (Bremsstrahlung) with a minimum wavelength of -0.155

A

and the

characteristic X-ray spectrum of tungsten

11. What is the de-Broglie wavelength (in

A)

of the a-particle

accelerated through a potential difference V ?

(a) 0.287

-JV

( ) 0.101 c

.Jv

(b) 12.27

-JV

'

(d) 0.22

-JV

12. An oil drop carrying a charge q has a mass m kg. It is

falling freely in air with terminal speed v. The electric

field required to make the drop move upwards with the same speed is (a) mg q (c) mgv

7

(b) 2mg (d) q 2mgv q

13. ·Photons of energy of 6 eV are incident on a metal surface whose work function·is.4 eV. The minimuin kinetic energy

. ofthe emitted photoelectronn~ill be

(a) Zero

(c) 2 eV

(b) 1 eV

(d) 10 eV

14. The de-Broglie wavelengthL associated with an elementary particle of linear momentum p is best represented by the graph L L (a) (b) p p L L (c) (d)

~

p p

15. Maximum velocity of photoelectron emitted is 4.8 ms-1.

The e/m ratio of electron is 1. 76 x 1011 _{Ckg-1, then}

stopping potential is given by

(a) 5x10-10_Jc-1 _{(b) 3x10-}7 _Jc-1 (c) 7x10-11Jc-1 _{(d) 2.5x10-}2_Jc-1

16. Two identical metal plates shown photoelectric effect by a light of wavelength

leA

falls on plate A and _{'A8 on plate}

B('AA = 2'A_{8 )}. The maximum kinetic energy is

(a) 2 KA = _K8 (b) KA < _K8 /2

(c) KA= 2KB (d) KA = _K8 /2

17. During X-ray production from coolidge tube if the current is increased, then

(a) the penetration power increases (b) the penetration power decreases (c) the intensity of X-rays increases (d) the intensity of X-rays decreases

18. Light of wavelength 5000

A

falls on a sensitive plate with photoelectric work fi.mctional of 1. 9 eV. Th€ kinetic energy

of the photoelectron emitted will be

(a) 0.58 eV (b) 2.48 eV (c) 1.24 eV (d) 1.16 eV

19. A proton and an a-particle are accelerated through the same potential difference. The ratio of their de-Broglie wavelength ('AP!'A0) is

(a) 1!

2.fi

(b) 1

(c) 2 (d)

2.J2

20. The de-Broglie wavelength of a neutron at 27°C is A..

What will be its wavelength at 927°C?

(a) A/4 (b) A/3

(c) A/2 (d) 3 A/2

21. A potential difference of 104 Vis applied across an X-ray tube. The ratio of the de-Broglie wavelength of X-rays produced is

(!...

for electron = 1.8 x 1011 _Ckg-1)

1 r a ) -' 20 (c) 1 m 1 (b) 10 1 (d) 100

22. The minimum light intensity that can be perceived by the eye is about 10-10 wm-2. The number of photons of wavelength 5.6 x 10-7 m that must enter the pupil of area 10-4 m3s-1, for vision is approximately equal to (h = 6.6 x 10-34 J-s)

(a) 3 x 102 photons (c) 3_x 104 photons

(b) 3 x 103 photons (d) 3 x 105 photons

23. A charged oil drop falls with terminal velocity v0 in the absence of electric field. An electric field E keeps it stationary. The drop acquires charge 3q, it starts moving upwards with velocity v_{0 .} The initial charge on the drop

lS (a) q/2

(c) 3q/2

(b) q (d) 2q

24. The filament current in the electron gun of a coolidge tube is increased while the potential difference used to accelerate the electrons is decreased. As a result, in the emitted radiation

(a) the intensity increases while the minimum wavelength decreases

(b) the intensity decreases while the minimum wavelength increases

(c) the intensity as well as the winimum wavelength increases

(d) the intensity as well as the minimum wavelength decreases

25. What is the strength of transverse magnetic field required to bend all the photoelectrons within a circle of a radius 50 em. When light of wavelength 3800

A

is incident on a barium emitter? (Given that work function of barium is 2.5 eV; h = 6.63 x 10-34 J-s; e = 1.6 x 10-19 C ;

m = 9.1

x

10-31 _kg.)

(a) 6.32 X 10-4 _{T (b) 6.32 X 10-}5 _T (c) 6.32 X 10--6 T (d) 6.32 X 10--8 T

26. Given that a photon of light of wavelength 10,000

A

has an energy equal to 1.23 eV. When light of wavelength 5000

A

and intensity I₀ falls on a photoelectric cell, the surface current is 0.40 x 10--D A and the stopping · potential is 1.36 V, then the work function is

(a) 0.43 eV (b) 0.55 eV (c) 1.10 eV (d) 1.53 eV

2 7. The wavelength of characteristic X-ray Ka.line emitted by hydrogen like atom is 0.32

A.

The wavelength of Kp line emitted b;r the same element is o

(a) 0.21 A (b) 0.27 A

(c) o.33

A

Cd) o.4o

A.

28. A photon and electron have same de-Broglie wavelength. Give that v is the speed of electron and c is the velocity of light . Ee, EP are the kinetic energy of electron and photon respectively. Pe• Ph are the momentum of electron and photon respectively. Then which of the following relation is correct? (a)

~=

-v (b)

Ee

= -2c

EP

2c

_EP

v ~=~ (d) ~= 2c (c) -Ph 2v Ph v

29. Which one of the following. statements regarding photo-emission of electrons is correct?

Chapter 26

•

Electron and Phofon

1001

(a) Kinetic energy of electrons increases with the intensity of incident light.

(b) Electrons are emitted when the wavelength of the incident light is above a certain threshold wavelength.

(c) Photoelectric emission is instantaneous with the incidence of light.

(d) Photoelectrons are emitted whenever a gas is irradiated with ultraviolet light.

30. A 100 W light bulb is placed at the centre of a spherical chamber of radius 0.10 m. Assume that 66% of the energy supplied to the bulb is converted into light and that the surface of chamber is perfectly absorbing. The pressure exerted by the light on the surface of the chamber is (a) 0.87 X 10--6 Pa (b) 1.77 X 10--6 Pa (c) 3.50 x 10--6 Pa (d) None of these

May have More than One Correct Option

31. When photons of energy 4.25 eV strike the surface of a metal, the ejected photoelectrons have a maximum kinetic energy EA eV and de-Broglie wavelength A.A- The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.70 eV is E₃ = (EA -l.SO)eV. If the de-Broglie wavelength of these photoelectrons is 'AB = 2'AA, then

(a) the work function of A is 2.25 eV (b) the work function of B is 4.20 eV

(c) EA = 2.0 eV (d) E₈ = 2.75 eV

32. In Thomson's experiment, if the velocity of electron is greater than the ratio of electric field (E) and magnetic field (ie, v > E!B), then

(a) the electron will reach the undeflected spot (b) the electron will not reach the undeflected spot (c) the electron will move to a spot above the undeflected

position

(d) the electron will move to a spot below the undeflected position

33. When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons heyve maximum kinetic energy TA eV and de-Broglie wavelength A.A. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is T₈ = (TA - 150) eV. If the de-Broglie wavelength of these photoelectrons 'AB = 2'AA, then

(a) the work function of A is 1.50 eV (b) the work function of B is 4.0 eV (c) TA = 2.00 eV

(d) All of the above

34. Electric conduction takes place in a discharge tube due to movement of

(a) positive ions (b) negative ions (c) electrons (d) photons

35. The maximum KE of photoelectrons ejected from a photometer when it is irradiated of wavelength 400 nm is 1 eV. If the threshold energy of the surface is 0.9 eV (a) the maximum KE of photoelectrons when it is

irradiated with 500 nm photons will be 0.42 eV (b) the maximum KE in case (a) will be 1.425 eV (c) the longest wavelength which will eject the

photoelectrons from the surface is nearly 650 nm (d) maximum KE will increase if the intensity of radiation

I

1002

Chapter 26

•

Electron and Photon

Comprehension

Based Questions

Passage I

According to Einstein, when a photon or light of frequency v or wavelength A is incident on photosensitive metal

surface of work function <j>_{0 ,} where <Po < hv (here h is

Planck's constant), then the emission of photoelectrons

takes place. The maximum kinetic energy of the emitted

photoelectrons is given by Km,; = hv-<j>_{0 •} If the frequency

of the incident light is v₀ (called threshold frequency),

the photoelectrons are emitted from metal without any

kinetic energy. So hv₀ =<Po

36. Stopping potential of emitted photoelectron is given by (a) hv-<Po (b) hv-<Po

e

hv

(c) (d) <Po+hv

e e

37. The variation of maximum kinetic energy CKmax) of the emitted photoelectrons with frequency (v) of the incident radiations can be represented by

Kmax Kmax

(a)~'

(b)

Kmax Kmax

(c) (d)

Passage II

Acco-rding to de-Broglie, a moving material particle exhibits dual nature (ie, a particle as well as a wave). He also predicted that a wave is associated with every

moving material particle (which controls the particle)

called matter wave and its wavelength is called de-Broglie

wavelength given by

A= h!mv

where h is Planck's constant, m is the mass of the particle

moving with velocity v.

The existence of matter waves was firstly experimentally

verified by Davisson and Germer using slow moving electrons which were accelerated with moderate accelerating potential.

38. An electron is accelerated under a potential difference of 64 V, the de-Broglie wavelength associated with electron is (use charge of electron 1.6 x 10-19 C, mass of electron

9.1 x 10-31 kg; h = 6.623 x 10-34 J-s). (a) 1.53

A

Cb) 2.53

A

Cc) 3.35

A

Cd) 4.54

A

39. If a-pa ide and proton have ·same momenta, the ratio of de-Broglie wavelength of a,particle and proton is

(a) 2 (c) l/2

(b) 1 (d) 1/4

40. If a-particle and proton are accelerated through the

same potential difference, then the rati,o of de-Broglie wavelength of a-particle and proton is

(a)

J2

(b) 2J2

1 ( c )

-2J2

Assertion and Reason

1

(d)

J2

Directions Question No. 41 to 50 are Assertion-Reason type. Each of these contains two Statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choice, only one of which is correct. You have to select the correct choices from the codes (a), (b),

(c) and (d) given below:

(a) If both Assertion and Reason are true and the Reason is

correct explanation of the Assertion.

(b) If both Assertion and Reason are true but Reason is not correct explanation of the Assertion.

(c) If Assertion is true but Reason is false. (d) If Assertion is false but the Reason is true.

41. Assertion The cathode of a photoelectric cell is changed such that the work function changes from W₁ to W₂

(W₂ > W_1). If current before and after change are 1₁ and

1₂ all other conditions remaining unchanged (assuming

hv > W₂₎ then 1₁ < 1₂.

Reason In above case 1₁ = 1_{2 .}

42. Assertion Work function of copper is greater than the work function of sodium, but both have same value of threshold frequency and threshold wavelength.

Reason The frequency is inversely proportional to wavelength.

43. Assertion Photocells are used in cinematography. Reason A photocell converts electrical energy into light energy.

44. Assertion A tube light emits white light.

Reason Emission of light in a tube takes place on a very high temperature.

45. Assertion The de-Broglie wavelength of a molecule varies inversely as the square root oftemperature.

Reason The root mean square velocity of the molecule depends on the temperature.

46. Assertion Stopping potential ·is a measure of KE of photoelectron.

1

Reason W = eV₅ = -mv2

= KE

2

47. Assertion The graph of stopping potential (VJ versus frequency (v) of incident radiation is a straight line nor passing through the origin.

Reason According to Einstein's photoelectric equation the slope of the graph between V₅ and ,. is

!!:_.

e

48. Assertion A photon has no rest mass, yet it carries definite momentum.

Reason Momentum of photon is due to energy hence its equivalent mass.