An electrical pump excites an atom from ground state energy 0 = 0 eV to an upper

Question

An electrical pump excites an atom from ground state energy 0 = 0 eV to an upper energy state 2 = 1.3 eV in an average time 02 = 18 ps. This atom will spontaneously decay from state 2 to an intermediate energy state 1 = 0.8 eV in an average time 21 = 3 ps. The lasing transition is from state 1 to the ground state 0.

a.) What is the frequency of a photon emitted in the lasing transition?

b.) Estimate the maximum energy width 1 that state 1 can have so that spontaneous emission is slow enough for the pump to generate a population inversion between states 1 and 0.

Explanation / Answer

(a)

hv = e1 - e0 , where h is plank's constant and v is the frequency of the lasing transition.

v = 0.8 eV / h

v = 1.93 * 10^(-14) hz

(b)   

From Heisenberg Uncertainty principle,

del e1 * del t = hbar, where del e1 is uncertainty in e1, del t is average lifetime of atom in e1 state and hbar = h/(2*pi)

del e1 = hbar / del t

= 1.054 * 10^(-34) / 3 * 10^(-12)

= 0.00022 eV

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