Class XI

Structure of atom

Content

• Sub atomic particles

• Ruther ford’s atomic Model

• Black body radiations

• Plank’s quantum theory

• Photoelectric effect

• Bohr’s atomic model

• De-Broglie’s equation

• Heisenberg’s uncertainty principle

• Quantum number

• The first atomic theory was proposed by John Dalton on the basis of the law of conservation of mass and law of definite proportions. He regarded the atom as the ultimate particle of matter.

• J.J Thomson discovered electron and he calculated charge to mass ratio for electron (e/m = 1.76 x 1011 C kg-1). The e/m ratio is also called specific charge and was found to be independent of the nature of gas and electrode used.

• Thomson also proposed atomic model in which he assumed the atom possesses a spherical shape radius approximately (10–10 m) in which the positive charge is uniformly distributed. This model is also known as raisin pudding model. It explained the stability and electrical neutrality of atom.

• Goldstein discovered anode (or positive or canal) rays. The specific charge of anode rays was found to vary with nature of gas. If H2 is used, then these positively charged particles are called protons. Ruther ford’s Atomic model

• While bombarding the gold foil with high speed, α particles, Ruther ford noticed that i. Most of the α particles passed without any deflection ii. Some of the α particles were deflected from its path. iii. A very few α-particle (∼1 in 20,000) bounced back, i.e., were deflected by nearly

1800. • On the basis of the observations Rutherford drew the following conclusions regarding

the structure of atom: i. Most of the space in atom is empty. ii. The presence of positively charged nucleus at the centre, with all its protons. iii. Electrons are present in the extra nuclear part of atom that moves around the

nucleus with high speed in circular orbits. iv. Electrons and nucleus are held together by electrostatic force of attraction.

• The ideal body, which emits and absorbs all frequencies is called a black body and the radiation emitted by this body are called black body radiations. The exact frequency distribution of emitted radiations from a black body depends upon its temperature.

• According to Planck’s quantum theory, the energy is emitted or absorbed only in descrete units or packets of energy called photon (or quantum). The energy of one photon is given by:-

E = hv Where v = frequency and h = Planck’s constant

or E = hc

λ

Where h = Planck’s constant and has the value 6.626 x 10-34 js

• Electrons come out as soon as a beam of light falls on the surface of the metal if the frequency of incident light is greater than threshold frequency.

hν = hνo + K.E Concept of Photon: A particle travelling with the speed of light must be mass less (rest mass, mo = 0) or its effective mass during motion will be infinite.

m = 22

o

/c1

m

v−

Note : Photoelectric effect explains the particles nature of light. But light has both wave and particles properties i.e. it has dual nature.

Bohr’s Atomic Model: • Bohr’s model was given in order to remove the drawbacks of Ruther ford’s model. The

main postulate of the Bohr’s theory are:- i. The electron in the hydrogen atom can move around the nucleus in a circular path of

fixed radius and energy. These paths are called orbits. ii. As long as electron stays in the same orbit, it does not radiate energy.

The emission or absorption of energy takes place only when the electron jumps from one energy level to another. This takes place in the form of photons. ∆E = E2 - E1 = hv

iii. The angular momentum of electron in closed cell is quantized.

2

nh

π = mvr

• According to Bohr’s theory of hydrogen atom I. The stationary states for electron are given as n = 1, 2, 3. these integral numbers are

known as principal quantum numbers. II. Expressions for radius, energy and velocity of electron moving in nth orbit of hydrogen

atom (or hydrogen like species).

1. ( )

πεπ=

0

22

22

4/Zem4h

nr = 0.529 × Zn2

Å

2. ( )

πεπ−=2

2

0

22

2 h4/eZm2

n1

E = – 21.8 × 10–12 × 2

2

nZ

erg per atom

= – 13.6 × 2

2

nZ

eV per atom = – 313.6 × 2

2

nZ

Kcal per mol

3. ( )

nh4/eZ2 0

2 πεπ=ν = 2.18 × 108 × nZ

cm/sec.

• The expression of spectral transitions is

∆E = Z2 Rhhc

−

2

2

2

1 n1

n1

where RH, known as Rydberg constant,

RH =( ) 17

3

2

0

22

m1009678.1ch

4/em2 −×=πεπ

Hydrogen Spectra

• The emission spectrum of hydrogen was first studied by Bohr in 1914. The situation in this case being simplified by the fact that the hydrogen atom has only one electron. the spectrum of hydrogen consists of five sets of discrete lines occurring in the ultra-violet, visible and infra-red regions of the electromagnetic spectrum. These sets are known as Lyman series, Balmer series, Paschen series, Brackett series and Pfund series, after the men who detected them.

• It was also found that the lines in the series were related to one another and could be represented in a single formula

−=22H m

1n1

Rλ

1

λ is the corresponding wavelength, RH is a constant (Rydberg constant), n and m are whole numbers related to the series as follows:

Lyman series n = 1 M = 2, 3, 4 … Balmer series n = 2 m = 3, 4, 5 … Paschen series n = 3 m = 4, 5, 6 … Brackett series n = 4 m = 5, 6, 7 … Pfund series n = 5 m = 6, 7, 8 …

• Bohr model failed to i. Explain the spectra of atom containing more than one electron. ii. Explain the fine structure in the spectrum of H – atom using high resolution

spectroscopic techniques. iii. Explain the ability of atoms to form molecules by chemical bonds

• The important discoveries which results in the failure of Bohr model were: i. Dual behavior of matter i.e., De Broglie’s Equation: According to which electron

has a dual character, both as a material particle and as a wave. Wavelength λ, of a particle of mass m, moving with velocity V is expressed as

λ = mVh

(h = Planck’s constant)

ii. Heisenberg uncertainty principle i.e., According to this principle “it is not possible to determine precisely both the position and the momentum ( or velocity) of a

microscopic moving particle”. Mathematical expression is ∆∆∆∆x ××××∆∆∆∆p ≥≥≥≥ 4πh

• In an atom, large numbers of orbital are possible which can be distinguished by size, shape and their orientation. Each orbitalis defined by three quantum numbers, n, l and m

i. Principle quantum number (n) determines the size of atom, the number of orbitals in a given shell (n) = n2 and its value varies 1 to n.

ii. Azimuthal quantum number ( l) defines the three dimensional shape of the orbital. For the given value of n, l can have n values ranging from 0 to n-1.

iii. Magnetic quantum number determines the orientation of orbital in space, the number of values of m is given by 2 l + 1. Its value varies from – l to 0 to + l

iv. Spin quantum number determines the spin of an electron. It has two values. S = 1/2 (clockwise direction), s = -1/2 (anticlockwise direction)

• Electrons are filled in to various orbitals in order to increasing energy. This is known as

the Aufbau’s principle. The energy of orbital depends upon (n + l) value. The increasing order of energy of orbital is 1s < 2s <2p < 3s < 3p < 4s < 3d < 4p <5s< 4d < 5p <6s < 4f < 5d <6p <7s <5f <6d <7p

• Orbitals of same energy are called degenerate orbitals (like px, py, pz)and according to Hund’s rule of maximum multiplicity no pairing of electrons starts in degenerate orbitals until or unless each one is singly filled.

• The orbital can accommodate maximum of two electrons with opposite spins and no electrons in an atom can have same set of four quantum numbers. This is known as Pauli’s Exclusion principle.

• Orbital Angular Momentum of Electron:

L = π

+2h

)1(ll

l = azimuthal Q.N. = 0,1,2,3 ---------, for s,p,d,f ------------ sub – shells of orbitals, respectively

• Z - component of orbital angular momentum of an electron in an orbital is given by

π=

2h

mL

Where m = –l to +l including zero (only integral value) If θ be the angle between Z – axis and angular momentum vector then

L2 = L cosθ Or

π2h

m = π

+2h

)1(ll Cosθ

Or m = )1( +ll cosθ

Since m ≠ )1( +ll , so, θ ≠ 0

☛ Spin angular momentum of electron, Ls = 1)s(s + π2

h

☛ Number of possible spectral lines that may be emitted by a sample of one electron system

(atom or ion) containing all or some speeds excited to nth energy level = 2

1)n(n −

☛ Number of revolutions per second made by an electron in nth orbit = n

n

r2Vπ

= n