Question

Calculate the population of two states in He-Ne laser produces light of
wavelength 7000 Å at 27oC.

Answer 1

9 Standard Ka Question he kaya Yaha par

Answer 2

Given:

wavelength λ = 7000 Å

temperature T = 27°C

To find:

the ratio of the population of two states $\frac{N_1}{N_2}$ =?

Step-to-step-Explanation:

• The ratio of the population of two states is given by the Boltzmann distribution formula.
• The  Boltzmann distribution formula is as follows:

        $\displaystyle \frac{N_1}{N_2} = e^{\frac{-\triangle E }{kT}} }$                        ...(1)

        where

        $\frac{N_1}{N_2}$ =  the ratio of the population of two states

       ΔE = energy difference between two states

       k =  Boltzmann constant

       T = temperature

• But the energy difference between two states ΔE is given by

        $\displaystyle \triangle E = \frac{hc}{\lambda}$

        where

        h = Planck's constant

        c = speed of light

        λ = wavelength

• Put the given value in the above formula to calculate the energy difference.

       $\displaystyle \triangle E = \frac{6.63\times10^{-34}\times3\times10^8}{7000\times10^{-10}}$

       ΔE = 3.143 × 10⁻¹⁹ J

• Now, put these values in the above equation (1)

       $\displaystyle \frac{N_1}{N_2} = e^{\frac{-13.143 \times10^{-19} }{1.38 \times 10^{-23} \times 300}} }$

       $\displaystyle \mathbf {\frac{N_1}{N_2} = 1.1 \times 10^{-33}}$

Hence the ratio of the population of two states is 1.1 × 10⁻³³.