**NEET Physics Notes Optics -Atoms and Nuclei -Bohr’s Model**

**Bohr’s Model**

**Bohr’s added the following postulates to the Rutherford’s model of the atom**

- The electrons revolve around the nucleus only in certain permitted orbits, in which the angular momentum of the electron is an integral multiple of h/2π where h is the Planck constant.
- The electrons do not radiate energy while revolving in the permitted orbits.

i.e. the permitted orbits are’stationary, non-radiating orbits. - The energy is radiated only when the electron jumps from an outer permitted orbit to some inner permitted orbit. (Absorption of energy makes the electron jump from inner orbit to outer orbit)
- If the energy of the electron in nth and mth orbits be E
_{n}and E_{m}respectively, then while the electron jumps from nth to mth orbit the radiation frequency v is emitted, such that E_{n}– E_{m}= hv. - This is called the Bohr’s frequency equation.

**Some Characteristics of an Atom**

- The orbital radius of the electron is

- The orbital velocity of electron is

- Orbital frequency is given by

**Hydrogen Spectrum**

Hydrogen spectrum consists of spectral lines classified as five spectral series of hydrogen atom. Out of these five, Lyman series lies in the ultraviolet region of spectrum, Balmer series lies in the visible region and the remaining three series, lie in the infrared region of spectrum.

The five spectral series of hydrogen atom are given below

**Lyman Series**

Spectral lines of Lyman series correspond to the transition of electron from higher energy levels (orbits) = 2,3,4,.. .to ground energy level (1st orbit) = 1 For Lyman series

It is found that a term Rch = 13.6 eV= 2.17x 10 18 J. The term Rch is known as Rydberg’s energy.

**Balmer Series**

Electronic transitions from = 3, 4,5,… to = 2, give rise to spectral lines of Balmer series.Thus, for a Balmer series line

where, n = 3, 4,5……

**Paschen Series**

Lines of this series lie in the infrared region and correspond to electronic transition from =4,5,6,…to =3

where n = 4, 5, 6.

**Brackett Series**

It too lies in the infrared region and corresponds to transition from= 5,6,7,…… to = 4.

Thus, for Brackett series

**Pfund Series**

It lies in the far infrared region of spectrum and corresponds to electronic transitions from higher orbits =6,7,8,…to orbit having = 5. Thus, we have

**Ionisation Energy and Potential**

Ionisation energy of an atom is defined as the energy required to ionise it i.e. to make the electron jump from its present orbit to infinity. Thus, ionisation energy of hydrogen atom in the ground state

The potential through which an electron is to be accelerated, so that it acquires energy equal to the ionisation energy is called the ionisation potential.

Therefore, ionisation potential of hydrogen atom in its ground state is 13.6V.

**Excitation Energy and Potential**

Excitation energy is the energy required to excite an electron from a lower energy level to a higher energy level. The potential through which an electron is accelerated, so as to gain requisite ionisation energy is called the ionisation potential.

Thus, first excitation energy of hydrogen atom = E2-E_{1}=-3.4- (- 13.6)eV = + 10.2eV

Similarly, second excitation energy of hydrogen atom

= E3 – E_{1} = -1.51- (-13.6) = 12.09eV