Question

Find the ratio of population of two energy levels in a Laser if the transition between them produces light of wavelength 800 nm. Assume the ambient temperature to be 27° C.​

Answer 1

Explanation:

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Answer 2

Answer:

The ratio of  population of two energy levels in the given laser will be equal to 1.142×10²⁶.

Explanation:

Given:

Wavelength of laser light, $\lambda=800nm=8*10^{-7}m$

Ambient temperature , $T=300K$

To find the ratio of population of energy levels:

$\frac{N_{2}}{N_{1}}=e^{\frac{E_{2}-E_{1}}{K_{B}T}$

where $K_{B}=1.38*10^{-23}JK^{-1}$

Where $E_{1}-E_{2}$ =ΔE $=\frac{hc}{\lambda}$

Therefore ΔE  $=\frac{(6.626*10^{-34}Js)(3*10^{8}m)}{8*10^{-7}ms^{-1}}$

ΔE $=2.485*10^{-19}J$

Ratio of population:

$\frac{N_{2}}{N_{1}}=e^{[\frac{2.485*10^{-19}J}{(1.38*10^{-23}JK^{-1})(300K) }]$

$\frac{N_{2}}{N_{1}}=e^{60}$

$\frac{N_{2}}{N_{1}} =1.142*10^{26}$

Therefore the ratio of population will be 1.142×10²⁶.