Question

6. Calculate the energy separation in joules and reciprocal centimeters between levels (a) n 2 and n-1 and (b) n = 6 and n 5 of an electron in a box of length 1 nm. What can you conclude about the energy separation as a function of quantum number for particle in a box model. Does this make sense, explain?

Answer 1

6.

(a)

$E_n=\frac {n^2\pi^2 \hbar^2 }{2ml^2}$

$E_2-E_1=\frac {(2^2-1^2)\pi^2 \hbar^2 }{2ml^2}=\frac {3\pi^2 \hbar^2 }{2ml^2}$

(b)

$E_6-E_5=\frac {(6^2-5^2)\pi^2 \hbar^2 }{2ml^2}=\frac {11\pi^2 \hbar^2 }{2ml^2}$