Answer:
The spectral half-width is 11.1 nm.
Explanation:
we know that if f is the frequency and h is the planck constant, then the energy is given by:
E = h×f
but if c is the speed of light and λ is the wavelength then, f = c/λ.
E = [h×c]/λ
λ = [h×c]/E
then the change in λ is given by:
Δλ = [(h×c)/(E^2)]×ΔE
= [(h×c)/((h×c/λ)^2)]×ΔE
= [(λ^2)/(h×c)]×ΔE
but we also know that:
ΔE = 1.8×k×T , where k = 1.38×10^-23J/K and T = 20 + 273 = 293K
then the half-width is given by:
Δλ = [(λ^2)/(h×c)]×1.8×kT
= [((550×10^-9)^2)/((6.63×10^-34)×(3×10^8))]×1.8×(1.38×10^-23)×(293)
= 1.11×10^-8 m
≈ 11.1 nm
Therefore, the spectral half-width is 11.1 nm.
