Question

The ground state of an oscillator is 10 meV. How much energy is
needed to excite this oscillator to the first excited state? If this oscillator is in thermal
equilibrium at 300 K, calculate the energy of the system

Answer 1

Solution

Ground state energy of an Oscillator is

$E_0=\frac{\hbar \omega}{2}=10\times10^{-3}eV$

First excited state is given

$E_1=\frac{3\hbar \omega}{2}=3\times10^{-2}eV$

Thermal energy is given

$E= kT=1.38\times10^{-23}\times300$

$E=4.14\times10^{-23}eV$