Answer to Question #117515 in Quantum Mechanics for Mr. A. Rangaraja Nayak

Question

quantum simple harmonic oscillator consisting of an electron under the influence of an restoring force was found to make a transition from n=2 state to n=3 state after absorbing a photon of wavelength 550 nm. Find the proportionality constant k for the oscillator. Mass of an electron =9.1x10-31 Kg; Planck’s constant=6.63x10-34 Js; speed of light in vacuum=3.0x108 m/s

Answer 1

$$E=k(n+0.5)$$

$$E_2-E_1=1.5k=\frac{hc}{\lambda}$$

$$1.5k=\frac{(6.63\cdot10^{-34})(3\cdot10^{8})}{550\cdot10^{-9}}$$

$$k=2.41\cdot10^{-19}J$$