An atomic level has a lifetime, τ, of . What is the linewidth, , of this level?

Question

An atomic level has a lifetime, τ, of  . What is the linewidth,  , of this level?

Quizplus · Accepted Answer

The linewidth of an energy level, ΔE, can be found using the uncertainty principle, which states: ΔEΔt ≥ h/4π.

Rearranging, we get: ΔE ≥ h/4πΔt

Substituting the given values, we get: 
ΔE ≥ (6.626 x 10^-34 J s)/(4π x 11 x 10^-6 s) = 4.77 x 10^-30 J

Converting to frequency using the formula, E = hf, we get:
f = ΔE/h = (4.77 x 10^-30 J)/(6.626 x 10^-34 J s) = 7.20 x 10^3 Hz

Converting to wavelength using the formula, c = λf, where c is the speed of light, we get:
λ = c/f = (3 x 10^8 m/s)/(7.20 x 10^3 Hz) = 4.17 x 10^-5 m

Converting to scientific notation and rounding to four significant figures, we get: 
Δν = 4.17 x 10^-5 m = 11eb6adc_edb9_5f5b_b0cf_33644234359a_TB8245_11.

Therefore, the answer is B.

An Atomic Level Has a Lifetime, τ, of