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Alika [10]
3 years ago
9

The energy levels of a quantum harmonic oscillator are given by En = n + 1 2 ¯h ω where 2π ¯h = h and h is Planck’s Constant. Th

e energy of a quantum of electromagnetic radiation (a photon) is Eλ = h c λ where λ is the wavelength of the radiation and c is the speed of light. If a harmonic oscillator transitions down one energy level, what is the wavelength of electromagnetic radiation emitted?
Physics
1 answer:
PolarNik [594]3 years ago
5 0

Answer:

2πc/w

Explanation:

To find the wavelength you take into account the difference in energy of two adjacent states n+1 and n:

E_{n+1,n}=\hbar \omega((n+1)+\frac{1}{2})+\hbar \omega(n+\frac{1}{2})\\\\E_{n+1,n}=\hbar \omega(1)

hbar = h/2π

this energy is also the energy of an emitted photon in the transition, that is:

E_{\lambda}=h\frac{c}{\lambda}   (2)

you equal the equations (1) and (2) and compute the wavelength:

E_{\lambda}=E_{n+1,n}\\\\h\frac{c}{\lambda}=\frac{h}{2\pi}\omega\\\\\lambda=\frac{2\pi c}{\omega}

hence, the wavelength of the emitted photon is 2πc/w

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