An electron in a harmonic oscillator potential well and the value of the corresponding spring constant is 12.5 N/m.What is the wavelength of light emitted when the electron jumps from one level to the next?
A)419 nm
B)509 nm
C)572 nm
D)659 nm

Question

Quizplus · Accepted Answer

The energy difference between two neighboring energy levels in the harmonic oscillator is given by:
ΔE = hν = hc/λ
where h is Planck's constant, ν is the frequency of the emitted light, c is the speed of light, and λ is the wavelength of the emitted light.
The spring constant k of the harmonic oscillator potential well is related to the oscillation frequency ν by:
ν = (1/2π)·(k/m)^(1/2)
where m is the mass of the particle (in this case, the electron).
Using the given value of k = 12.5 N/m and the mass of the electron, we can calculate the frequency of the emitted light:
ν = (1/2π)·(12.5 kg/s^2 ÷ 9.109 × 10^-31 kg)^(1/2) = 2.42 × 10^15 Hz
Substituting this value into the first equation, we get:
λ = hc/(ΔE) = (6.626 × 10^-34 J·s)·(3.00 × 10^8 m/s)/(2.42 × 10^15 Hz) = 5.09 × 10^-7 m = 509 nm

An Electron in a Harmonic Oscillator Potential Well and the Value