GATE 2021 PH – Question 34
For the three-level atom shown, the Einstein spontaneous-emission coefficients are $A_{2\to1}=2\times10^7\ \mathrm{s}^{-1}$ and $A_{1\to0}=10^8\ \mathrm{s}^{-1}$. If $10^{14}$ atoms/cm³ are excited from level 0 to level 2 and a steady-state population in level 2 is achieved, the steady-state population in level 1 is $x\times10^{13}$ cm⁻³. Find integer $x$.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2 to 2
Explanation
At steady state, the rate entering level 1 equals the rate leaving it: $A_{2\to1}N_2=A_{1\to0}N_1$. With the maintained upper-level population $N_2=10^{14}$ cm⁻³, $N_1=(2\times10^7/10^8)10^{14}=2\times10^{13}$ cm⁻³. Thus $x=2$. The maintained-population condition is necessary; a single unpumped excitation would decay rather than remain in steady state.