Question

Consider a microscopic springmass system (with a single spring and a single mass) whose spring stiffness is k = 50 N/m and mass is m = 4 × 10−26 kg. a. What is the smallest amount of vibrational energy that can be added to this system? b. In a collection of microscopic oscillators, the temperature is high enough that the ground state and the first three excited states are occupied. What are the possible energies and wavelengths of the photons emitted by the oscillators.

Answer 1

Given is:-

Spring constant K = 50N/m

mass  

Now,

part -a

Using the relations  

or

eq-1

where

by plugging all the values in eq-1 we get

This is the smallest amount of vibrational energy that can be added to the given system

Part - b

The possible energies of photons emitted by these oscillators is,

Energy of highest energy photon will be

We also know that   or

by plugging all the values we get the required wavelength

which gives us

similarly

Energy of the next highest photon is

and the wavelength is

and the energy of the lowest photon is

and