Question

An electron is confined to a one dimensional region, bounded by an infinite potential. If the energy of the electron in its first excited state is 40 meV, what is its energy in its ground state? A. 40 me V B. 80 meV C. 20 meV D. O meV E. 10 meV

Answer 1

Answer:

The energy in its ground state is 10 meV.

Explanation:

It is given that,

The energy of the electron in its first excited state is 40 meV.

Energy of the electron in any state is given by :

$E=\dfrac{n^2\pi^2h^2}{8mL^2}$

For ground state, n = 1

$E_1=\dfrac{\pi^2h^2}{8mL^2}$.............(1)

For first excited state, n = 2

$40=\dfrac{2^2\pi^2h^2}{8mL^2}$.............(2)

Dividing equation (1) and (2), we get :

$\dfrac{E_1}{40}=\dfrac{1}{4}$

$E_1=10\ meV$

So, the energy in its ground state is 10 meV. Hence, this is the required solution.