Solved Problems of of Lasers

ANNA UNIVERSITY SOLVED PROBLEMS

Problem 5.1

Calculate the relative population of sodium atoms in sodium lamp in the first excited state and the ground state at a temperature of 250°C. ( λ= 590 nm)

Given data:

Planck's constant (h) = 6.625 × 10-34 Js

Velocity of light (c) = 3 × 108 ms-1

Boltzmann's constant (k) = 1.38 × 10-23 JK-1

Temperature T = 250°C = 250 + 273 = 523 K

Wavelength λ = 590 nm = 590 × 10-9 m

Solution:

Let N2 be the population of the first excited state and N1 be the population of the ground state.

We know that

Substituting the given values,

The ratio between the atoms in the first excited state and the ground state is 5.367 × 10-21.

Problem 5.2

Laser action occurs by transition from an excited state (E2) to the ground state (E1 = 0). If the transition produces a light of wavelength 6930 Å, find the energy level of the excited state.

Given data

λ = 6930 Å = 6930 × 10-10 m 

h = 6.625 × 10-34 Js 

c = 3 ×108 ms-1 

E1 = 0. (ground state))

Solution

Substituting the given values, we have

Energy of the excited state

Problem 5.3

Find the relative population of the two states in a ND - YAG laser that produces a light beam of wavelength 6943 Å at 300 K.

Given data

λ = 6943 Å = 6943 × 10-10 m

T = 300 K

Solution

The population ratio is given by

Problem 5.4

In a laser action the energy of the stimulated photon is 39.62 × 10-20 J. What is the wavelength of the stimulated photon?

Given data

Energy of the stimulated photon E = 39.62 × 10-20 J

Planck's constant h = 6.625 × 10-34 Js

Solution

We know that E = hv

Problem 5.5

Determine the wavelength of radiation given out by a laser with an energy of 3 eV, given that 

h = 6.63 × 10-34 Js and c = 3 × 108 ms-1. 

Given data

Energy (E) = 3eV = 3  × 1.6  × 10-19 J

h = 6.63  × 10-34 Js

c = 3  × 108 ms-1

Solution

We know that E = hv and

Substituting the given values, we have

Problem 5.6

Calculate the wavelength of light emission from GaAs whose band gap is 1.44 eV

Given data

Band gap Eg = 1.44 eV = 1.44 × 1.6 × 10-19J

h = 6.625 × 10-34 

c = 3 × 108 ms-1

Solution

Wavelength

Substituting given values,