ATOMIC STRUCTURE AND QUANTUM MECHANICS (UNIT-1)
Introduction
Chemistry is the science that deals with the composition, structure and properties of matter
Nature of Matter
Matter is considered as anything that occupies space, has mass and offers resistance.
Matter is classified as follows:
Based on physical state
Solid =have a definite shape and volume constitutes are closely packed and have less freedom of movement
Liquid =have a definite volume but no shape. Constituents are close to each other but are moving around. Gases =neither have definite shape nor volume. Constituents are far apart and can move freely.
Based on chemical composition
Element=pure substance that contain only one kind of atoms
Compound= chemical combination of two or more elements in a fixed proportion by mass Mixture= mixing of two or more compounds in any proportion
Homogeneous mixture = have a uniform composition throughout and the components are indistinguishable Heterogeneous mixture = do not have uniform composition and the components are distinguishable
Dalton’s Atomic Theory
The main points of Dalton’s atomic theory are as follows
1. Matter is made up of extremely small particles called atoms. The atoms are indivisible
2. All atoms of an element are identical, i.e. they possess same size, shape, mass, chemical properties, etc…
3. Atoms of different elements have different weights and different chemical properties
4. Atoms of different elements have different weights combine in ratios of simple whole numbers to form compounds
5. Atoms cannot be created nor destroyed.
*Atoms =Smallest particle of an element or that maintain its chemical identity through all chemical and physical changes is called atoms.
Molecules = is the smallest particle of an element or compound that can have a stable independent existence. In all molecules, two or more atoms are bonded together. If you take example such as oxygen. An atom of oxygen cannot exist alone at room temperature and atmospheric pressure. So single oxygen atom combine quickly to form diatomic molecule.
Polyatomic molecule – contain more than two atoms.
Atomic Structure Constitutes of an atom
A series of experiments performed by scientists like J.J.thomson, Rutherford, and Neil’s Bohr showed that atom consists of 3fundamental particles,
They are;
1. Electrons- Discovered by J.J Thomson in 1897 Symbol= e-
Mass (kg) =9.10939*10^-31 Approx mass(amu) =0 Relative charge = -1
2. Neutron – Discovered by J. Chadwick in 1932
Symbol = n or 0n 1
Mass (kg) =1.67493*10^-27 Approx mass (amu) = 1 Relative charge =0
3. Proton- Discovered by Goldstein in 1911 symbol= H+
Mass (kg) = 1.67262*10^-27 Approx mass (amu) =1 Relative charge == +1
Rutherford model of an atom or planetary model of an atom
Rutherford in 1910 bombarded a very thin gold foil of 10nm thickness with α-particle using a radioactive element Ra as a source and he kept ZnS screen to observe the deflection of α-particles by gold foil.
From this experiment he observed three things
1. A large fraction of α- particle passed through gold foil without any deflection. 2. Few α-particles are deflected minutely and at very small angles
From the above observation he concluded that;
1. Major space in an atom is empty
2. The positively charge in an atom is not distributed uniformly and it is concentrated in a very small volume.
3. The positively charged particles covered a small volume of an atom in comparison to the total volume of an atom.
Postulates of Rutherford atomic model based on observation and conclusion
1. An atom is composed of positively charged particles. Majority of the mass of an atom is concentrated in a very small region. This region of the atom is called as nucleus .(composed of neutrons and protons )
2. Atoms nucleus is surrounded by negatively charged particles called electrons. The electrons revolve around the nucleus in a fixed circular path called as orbits.
3. An atom has no net charge i.e. electrically neutral.
4. Size of nucleus is very small in comparison to the total size of an atom.
LIMITATIONS
1. Rutherford model was unable to explain the stability of an atom. According to Rutherford theory, electrons revolve around the nucleus in a fixed orbit. However, when a charged particle moves in an orbit, undergoes acceleration, according to Maxwell, charged particles when accelerated should emit radiations. Therefore an, electron in orbit will emit radiations and lose energy. The orbit shrinks and ultimately electrons would collapse in to the nucleus. But this does not happen. Hence, this model could not explain the stability of an atom.
2. If the electrons continuously emit radiations its atomic spectrum should be continuous. But the atomic spectrum is found to contain lines. i.e this model of atom is not able to explain line spectrum 3. It fails to explain the arrangement of electrons in the orbit.
Bohr’s model of an atom
Postulates of Bohr’s model
1. According to Bohr’s, an atom consists of positively charged nucleus in which entire mass is concentrated. Electrons are revolving around the nucleus in a certain definite circular orbits. These orbits do not emit radiant energy and are called stationary orbits.
2. Energy is emitted or absorbed by an atom only when electron moves from one level to other level ΔE=E2-E1. The energy is equal to difference in energy between these two energy levels. thus energy of an electron does not change abruptly. it changes only when it jumps from one energy level to other energy level.
3. The angular momentum of an electron is given by mvr
m—mass of electron v—velocity of electron
r—is the radius of orbit (distance between electron and nucleus)
angular momentum is an integral multiple of h/2π i.e . mvr= nh/2π where n=1,2, 3,….. etc.
based on these points. Bohr’s calculated the radius and energy of stationary orbit in hydrogen and hydrogen like atoms.
Hydrogen Spectrum
Bohr next improved a mechanism to explain the emission spectrum from hydrogen atom. It has one electron in K shell. If energy is supplied, electron absorbs energy and jump to higher levels (n=1,2,3,…..etc) depending upon the amount of energy absorbed . The electron jumps from one excited state to lower energy level, during which, energy is released. It’s observed in the form of emission spectrum.
If E1 and E2 are energies of ground state and excited state , then [since excited state is unstable , electrons will jump back to ground state by losing a quantum of energy ]
ΔE= E1- E2= hγ=hc/⅄
Greater the energy liberated, shorter is the wavelength of spectral line emitted.
During each transition, energy is released which appears in the form of radiations of specific frequency.
The wavelength of any spectral line in any series can be calculated using Rydberg’s equation.
Explanation of emission spectrum
1. Lyman series is obtained when electron jumps from higher energy level to first energy level (n=1) frequencies of lyman series can be calculated by substituting n1=1 and n2 =2, 3….. in above equation 2. Balmer series is obtained when an electron jumps from higher energy to second energy level so,
n1=2,and n2= 3,4,5,….
3. Similarly paschen, bracket series and pfund series are obtained when electron jumps from higher energy level to third, fourth, fifth energy levels( n=3, n=4, & n=5 etc)
n1=3,and n2= 4,5, 6… Table -1.1
Series n1 n2 region
Lymen 1 2,3,4,5,… Ultra-violet
Balmer 2 3,4,5,6,….. visible
Pschen 3 4,5,6,7….. Infra-red
Bracket 4 5,6,7,8,….. Infra-red
Pfund 5 6,7,8,9…. Infra-red
Limitations of Bohr’s model
1. According to Bohr, the radiation results when an electron jumps from one energy orbit to another energy orbit , but how this radiation occurs is not explained by Bohr
2. Bohr model explains well about position of lines in hydrogen spectrum , but it does not account for the fine structure.(i.e. when each line is observed under high resolution shows number of closely packed lines )
3. Bohr’s model enables us to locate both momentum and position in an orbital simultaneously. But this is not possible as per Heisenberg’s uncertainty principle
4. It also fails to explain the intensity of spectral line
5. The spectra of multi-electron systems could not be explained.
Velocity of electron in first orbit is given by the relation 𝐕𝟏 = 𝐧𝐡
𝟐𝛑𝐦𝐫
Velocity of electron in excited states can be obtained by taking n=2,3,4…..etc
The energy of the electron in nth orbit is given by 𝐄 = − 𝟐𝛑𝟐𝐙𝟐𝐦𝐞𝟒
(𝟒𝛑𝛆)𝟐𝐧𝟐𝐡𝟐
The Radius of nth orbit is given by 𝐫𝐧 =𝟒𝛑𝛆𝐨𝐧𝟐𝐡𝟐
𝟒𝛑𝟐𝐙𝐦𝐞𝟐 (4πεo =1.11264* 10-10 C2 N-1 m-2)
Problems
1.When it revolving in first orbit n=1 , its energy is obtained by the formulae
E1 = − 2π
2Z2Me4
(4πε)212h2
This energy is also known as energy associated with the orbit. Energy of first orbit is -1312.19Kj/mol
2. Calculate the energy of hydrogen atom is first excited state ,given 4πεo=1.11264X10-10 C2 N-1 m-2
Energy of first excited state, E2 = − 2π2Z2Me4
(4πε)222h2 = -328.04 Kj/mol
Plank’s Quantum Theory of Radiation BLACK BODY RADIATION
These curves have the following characteristics –
1. For each temp- there is a particular wavelength at which the energy radiated is the maximum. 2. The position of the maximum shifts towards the lower wavelengths, with increase in temperature. 3. Higher the temperature higher is the intensity of radiation
Quantum theory of radiation
Distribution was derived by Planck’s on the basis of the quantum theory of radiation. According to this theory
1. Radiant energy absorbed or emitted discontinuously in the form of tiny bundles of energy known as quanta
2. Each quanta is associated with a definite amount of energy i.e. E=hγ=hc/⅄
E = energy in joules
h= planck’s constant = 6.626X10-34 Js ⅄ =frequency of radiation
3. A body can emit or absorbed energy only in whole number multiples of quantum .i.e. 1h , 2h , 3h ,…etc nhγ.
Energy in fractions of a quantum cannot be lost or absorbed. This is known as quantization energy
Particle and Wave character (Dual nature) of electron According, to Einstein - light has dual character as wave and also a particle. According to de- Broglie- matter has a dual character as wave and also a particle
In Bohr theory electron is treated as a particle. But De-Broglie theory suggests that matter and therefore electron also has a dual character as wave and also as a material particle.
He derived an expression for calculating the wave length λ of a particle of mass m moving with velocity c according to which
λ =
𝐡𝐦𝐜 de Broglie equation
The de Broglie equation can be easily derived by using the mass-energy relationship. E=𝐦𝐜𝟐
Equating this equation with the energy of photon.
Quantum Mechanics
1. Classical mechanics deals with macroscopic particles such as planets and rigid bodies based upon neutron’s laws of motion.
2. It does not account for the fact that particle behave like waves in some circumstances
3. Position and momentum of the particle cannot be determined simultaneously which is not explained by classical mechanics
Quantum mechanics –
1. which deals with microscopic particles such as electrons , protons , atoms molecules show wave – particle duality. They do not obey newton’s dynamics
4. It takes in to account Heisenberg’s uncertainty principle, de-Broglie concept of dual nature of matter and Planck’s quantum theory
5. The laws of quantum mechanics were formulated in 1925 by Heisenberg’s and different scientists and in 1926 by the Austrian physicist Schrodinger
6. We cannot determine the exact position of an electron but according to quantum mechanics we can determine the probability of finding an electron at various places around the nucleus.
7. Quantum mechanical model orbitals are very different from a Bohr-orbit
8. A quantum mechanical orbit is a 3-D region of space , somewhat like the space inside a very small balloon ,an electron occupies a quantum mechanical orbital mush as a fly occupies a balloon it could be moving anywhere inside. A Bohr-orbit, it would behave like a train on a circular track – it would simply go round and round
Heisenberg’s Uncertainty Principle
In classical mechanics , by the definition itself a particle occupies a definite place in space and possesses a definite momentum . Knowing the particles position and momentum at any given instant of time, it is possible to evaluate its position and momentum at any later point of time. But when particle is traced continuously such a principle is breaks down in atomic scale
Quantum mechanics takes over for which one of the fundamental principles is the Heisenberg uncertainty principle
“It says that it is impossible to determine simultaneously both the position and momentum of a particle accurately “
If any effort made to measure very accurately of the position of the particle such as an electron results in a large uncertainty in the measurement of momentum and vice versa
Where the notation Δ in association with the respective variables, indicates the minimum uncertainty involved in the measurement of the corresponding variables.
Significance of Heisenberg’s Uncertainty Principles
One should not think of the position or an accurate value for momentum of a particle. Instead, one should think of the probability of finding the particle at a certain position or of the particle value for the momentum of the particle.
The estimation of such probabilities are made by means of certain mathematical functions, named probability density functions in quantum mechanics.
The Schrodinger Wave Equation Introduction
1. In 1926 Schrodinger gave a wave equation to describe the behaviour of electron waves on atoms and molecules.
2. In Schrodinger waves model of an atom the discrete energy levels of an orbits proposed by Bohr are replaced by mathematical function ,ψ which are related to the probability of finding electrons at various places around the nucleus
(calculation of the probability of the electron at various points in an atom was the main problem before Schrodinger)
3. The wave function describes properties of the orbital and the electron that occupies the orbital. From ψ we can determine the type of orbital that the electron occupies, the energy of the electron in that orbital (this energy is sometimes called the energy of the orbital ) , the shape of the orbital and probability of finding the electron in any particular region within the orbital.
4. We can describe the distribution of an electron in an orbital in terms of the electron density in various regions of the orbital. The electron density is high in those regions of the orbital where that probability is low. Although the electron might be located anywhere within an orbital at any instant in time , it spends more of its time in certain high probability regions.
5. The allowable patterns for electron waves can be described through Schrodinger wave equation
Where ψ is called wave function . wave functions contain three terms (called quantum numbers n, l, and m).where specific values are assigned to these three quantum numbers
The result is called an orbital; m—mass of the electron E—total energy of the electron v—potential energy of the electron h—planck’s constant
Wave function: fundamental particles such as electrons maybe described (as particles or waves) using a wave function i.e. ψ. The wave function is a mathematical expression. It carries crucial information about the electrons from wave function we obtain the electron energy, angular momentum and orbital orientations in the shape of the quantum numbers n, l and m.
Wave function ψ is related to the probability of finding electrons at various places around the nucleus
(calculations of the probability of electrons at various points in an atom was the main problem before Schrodinger ) the total wave function can be represented by the equation
Ψ=Aeikx−ωt (plane wave moving in the x-direction)
Where , A is a constant , and ω is the angular frequency of the wave
(wave function may vary with respect to both position and the time ).
The schrodinger equation can be set up in two different context. One which is general and takes care of both the position and time is called time dependent Schrodinger equation i.e.
− h2
8π2m∗ d2ψ
dx2 + Vψ=− ih 2π∗
dψ dt
Which involves the imaginary quantity ‘i’ .A wave function can have variation only with position but not with time . It is called time independent Schrodinger equation it is simpler than the other one i.e.
d2ψ dx2 +
8π2m
h2 (E − V)ψ = 0 It does not involve ‘i’
Time independent Schrodinger wave equation
The total wave function can be represented by the equation
ψ = Aei(kx−ωt) ----(1)
Differentiate the equation 1 w.r.t ‘x’
dψ dx = Ae
i(kx−ωt). ik
Differentiate once again w.r.t ‘x’
d2ψ
dx2 = Aei(kx−ωt). i2k2
d2ψ
dx2 = −K2Aei(kx−ωt)
d2 ψ
dx2 = −K
2ψ − − − (2)
Phase velocity V = W
K
K =W
V K—propagation constant or wave number ω = angular frequency i.e. ω=2πν
ν =V
λ =h
p (de Broglie eqn)
So equation (2) becomes
d2ψ dx2 = −
w2 v2 ψ
d2ψ
dx2 = −
4π2ν2
v2 ψ
= −4π
2ν2
ν2λ2 ψ
d2ψ dx2 = −
4π2
λ2 ψ = −
4π2p2
h2 ψ
p2ψ = − h2
4π2 d2ψ
dx2 --(4)
Total energy i.e. E is
E=K.E +P.E
= 1 2mv
2+ V
=m
2v2
2m + V
E = p
2
2m+ V
Eψ =p
2ψ
2m + Vψ
= − h
2m4π2
d2ψ dx2 + Vψ
= − h
2
8π2m
d2ψ
dx2 + Vψ
= − h
2
8π2m
d2ψ
dx2 = (E − V)ψ
d2ψ dx2 = −
8π2m
h2 (E − V)ψ
d2ψ dx2 +
8π2m
h2 (E − V)ψ = 0— (5)
This is the time independent schrodinger equation in one dimension
Significance Of Wave Function:( ψand𝛙𝟐)
The wave function ψ by itself has no physical significance except that it represents the amplitude of electron wave. Its square measures the probability of finding an electron of energy E at a particular place around the nucleus. (This region is called orbital.) The ψ2 is called the probability density, it is also called probability function.
Probability at any point must be a real and positive quantity. Hence in order to get a value that is positive and real while evaluating (ψ2). the wave function ψ is multiplied with its complex conjugate ψ∗ . The product ψ*ψ
Is always a positive real quantity and corresponds meaningfully to the definition of probability
Therefore probability density is given by:
ψ2 = ψ*ψ
ψ2 is the probability per unit volume that the particle will be found at the given region.
Quantum Numbers
To specify the position and energy of electron in the atom. Each electron in an atom is described by 4 quantum numbers. They give a complete address of an electron
1. Principle Quantum Number:(n)
It indicates the main energy level or shells to which electron belongs. It represents by symbol ‘n'
As the value of ‘n’ increases,distance between the electron and nucleus increases and energy increases.
The total number of electrons in a given main energy level is calculated by the formula2n2, where n is principle quantum number
It measures the size of an electron cloud
2. Azimuthal Quantum Number (l);
Each main energy level or shell is made up of number of sub shells
The number of sub shell in each main shell is given by azimuthal quantum number K –shell has one sub shell, L has 2 sub shells and so on
It indicates the shape of the orbital for a given value of ‘n’ azimuthal quantum number can have values l=0, 1, 2, 3,… (n-1).
(when more than one electron is present , its energy cannot be defined completely only by principle quantum umber but also requires azimuthal quantum number. Energy of electron in different orbitals is in the order of s<p<d<f.)
n 1,2,3,…….infinity
n1 First energy level or K shell
n2 Second energy level or L shell
n3 Third energy level or M shell
Principle quantum number (n)
Azimuthal quantum number (l)
Name of the orbital – Number of sub-shells
1 0 s –sub-shell One sub shell
2 0
1
s p
Two subshells
3 0
1 2 s p d 3 sub-shells
4 0
1 2 3 s p d f 4- sub-shells
3. Magnetic quantum number (m)
A main shell is made up of one or more sub shell and each sub shell is made up of one or more orbitals. Each orbital has a characteristics magnetic quantum number and can accommodate maximum of 2 electrons
It specifies the orientation of an orbital of a given energy (n) in space and shape (l). This number divides the sub shell into individual orbital which hold the electrons
For a given value of l, m, can have values –l to +l through zero i.e. –l,….-3, -2, -1,0, 1,+1, +2,……+l totally 2l+1 values
There are 2l+1 orbitals in each sub shell. Thus the s sub shell has only one orbital, the ‘p’ sub shell has 3 sub shells and so on
l=0(sub shell) m=0, one sub shell is present
l=1 (p sub shell) m=-1, 0 ,1 three orbitals are possible and they are Px, Py, Pz of same energy
l=2(d sub shell) m=-2,-1,0,+1,+2.. five orbital and they are dxy , dyz, dzx, dx2− y2 ,dz2
l=3(f subshell)m=-3,-2,-1,0,+1,+2,+3,
4. Spin Quantum numbers
It indicates the direction in which the electron is spinning about its axis i.e .in clockwise or in anticlockwise direction. it can have 2 values +1/2 or -1/2 . + Sign indicates clockwise spinning and – sign indicates anticlockwise spinning. an orbital can accommodate maximum of two electron of opposite spin ,
Possible values of, ‘l’ and ‘m’ for given value of ’n’,
n m l Symbols of orbitals
1 0 0 1s
2 0
1
0 -1.0.+1
2s 2p
3 0
1 2 0 -1,0,+1 -2,-1,0,+1,+2 3s 3p 3d
4 0
Shapes of orbital (or) Angular probability distribution curves
1. Shape of s orbital shape of s orbital is spherical. The size of orbital depends on the value of principle quantum number (n). Thus 2s orbital is larger than 1s orbital.
2. Shape of p- orbital :is dumb bell shaped , there are two lobes extending out into three dimensional space Since there are 3 p- orbitals in a given p sub shell the lobes extend out along x-axis (Px-orbital) , y-axis (Py orbital) and z-axis (Pz orbital) and are oriented along the three mutually perpendicular axes x,y,and z
3. Shape of d –orbital: they have double dumb bell shape. there are five degenerate d-orbital in d –sub shell
Pauli’s exclusion principle:
In order to explain the stability of electron in an orbital, Pauli postulated that ‘no two electrons in an atom can have all the four quantum numbers identical. That is in the same orbital of atom, two electrons cannot have all the four quantum numbers same, they differ in their spin quantum number.
Thus if s is +1/2 for one electron , s should be equal to -1/2 for the other electron in other words the 2 electron s in the same orbital should have opposite spins.
Thus maximum of 2 electrons are possible in one orbital, if third electron enters, it has same spin quantum numbers with one of the 2 electrons already present which is against to paulis exclusion principle.
ex; n=1, m=0, l=0, it is s orbital
n 1 1
l 0 0
m 0 0
s +1/2 -1/2
Therefore only two electrons are possible in one orbital with opposite spins.
Hunds Rule of Maximum Multiplicity:
“It states that pairing of electrons take place only after all the orbital of equal energy are half filled’’
Ex; electronic configuration of nitrogen is1s22s22p3. In p type all the p orbitals (Px, Py, Pz ) are of same energy . Each orbital takes on electron each.
Therefore electronic configuration of nitrogen is 1s22s22P1x 2P1y 2P1z In oxygen –1s22s22P2x 2P1y 2P2z
Filling Of Orbitals in Atoms:
The distribution of electrons in various orbitals is known as electronic configuration.
Aufbaus Principle : in ground state of atom , electron enters in to the orbital of lower energy before going to the orbital of higher .
The increasing order of energy of various orbitals is as follows: 1s<2s<2p<3p<4s<3d<4p<5d<4d<5p<6s………..
(n+l)rule , when the energy difference between two orbitals is very small , orbital with minimum (n+l) values is filled first this is called (n+l) rule where n= principle quantum number , l= azimuthal quantum number.
Ex : 1)for 4d orbital (n+l) =4+2=6 For 5s orbital (n + l )= 5+0=5
Therefore 5s orbital is filled before 4d orbital
When both orbitals have same (n+l) values, then orbital with lower ‘n’ value is filled first 2) 4f and 5d orbitals
For 5d orbital (n+l)=5+2=7
Therefore 4f orbital is filled first and then 5d orbital
ELECTRONIC CONFIGURATION OF FEW ELEMENTS
Elements Atomic number Electronic configuration
scandium 21 1s22s22p63s23p64s23d^1
Ti 22 [Ar]4s23d2
V 23 [Ar]4s23d3
Cr 24 [Ar]4s13d^5
Mn 25 [Ar]4s23d5
Fe 26 [Ar]4s23d6
Co 27 [Ar]4s23d7
Ni 28 [Ar]4s23d^8
Cu 29 [Ar]4s13d10
Zn 30 [Ar]4s23d^10
Probability Distribution Curve
In an atomic orbital there is a probability of finding the electron in a particular region at a given distance and in a particular direction from the nucleus
This gives rise to 2 types of probability of finding the electrons
1. From the curve for 1s electron it is evident that the value D is 0 when r=0 and infinity, ‘D’ increases as r value increase from zero, passes through a maximum at r=0.53A0and falls to zero as r tends to infinity . thus for 1s electron D=0 at r=0and infinity and D maximum at r=0.53A0
So the radius of maximum probability of 1s electron is 0.53A0
2. Curve for 2s electron, for 2s electron the value of D is zero when r is 0. The value of D increases as the r value increases, passes through a low maximum at r = r1 and falls to zero at r =2r1 . The value D increases as r increases from 2r1 and passes through second higher maximum at r=5r1=5X 0.53A0and finally approaches zero as r values tends to infinity. Thus for 2s orbital D is zero at r=0, r=2r1,∞. lower maximum lies at r =r1 and higher maximum lies at r= 5r1, so there is a greater probability of finding the electron further away from the nucleus.
3. For 2p electron – the maximum probability for 2p electrons is slightly less than that for the 2s electrons also the small addition peak for 2s indicates that 2s electrons penetrates a little closer to the nucleus than a 2p electron hence a 2s electron is attracted more strongly by the nucleus than a 2p electron. 2s is more stable than 2p electron (2s electron has lower energy than 2p electron).
QUESTION BANK
1. Illustrate the postulates and limitations of Bohr’s atomic model.
2. Explain the origin of the spectral lines of the hydrogen atom on the basis of Bohr’s atomic model. 3. Derive the Time independent Schrödinger wave equation and explain the terms.
4. Describe the angular probability distribution of s,p,d curves based on n and l value? 5. What are quantum numbers? Explain.
6. Write the electronic configuration of elements from atomic numbers 24 to 36. 7. What is Aufbau principle, (n+l) rule and why 4s orbital is filled before 3d orbital.
8. Derive de Broglie’s equation for matter wave and calculate wavelength of wave associated with mass 9.3X10 -31
kg moving with velocity of 5.4X106m/s ( given h=6,36X10-34Js) 9. Describe the planks quantum theory of radiation.
10. Illustrate the graphical representation of radial distribution of 1s, 2s, 3s, 2p, 3p and 3d electrons. 11. Draw the shapes of the orbital when l=0,l=1 and l=2
12. Define Hund’s rule and Pauli’s exclusion principle with example.
13. Calculate the wave number of the spectral line when an electron falls from n=4 to n=2. Given (R= 1.097X107m-1)
14. Write the significance of ψ,ψ2and sate Heisenberg’s uncertainty principle. 15. Calculate the energy of hydrogen atom in first and second excited state.
( given 4πƐ0= 1.1126X10 -10
