Question

With the increase in quantum number the energy difference between consecutive energy levels

• A. remains constant
• B. decreases
• C. increases
• D. sometimes increases sometimes decreases

Answer 1

Answer: (B)

decreases

The energy of an electron revolving in an orbit is:
$E=\frac{-m{e}^4}{8n^2{h}^2{ϵ}_0^2}$
where, variables have their usual meanings.
$\Rightarrow E_n\propto \frac{1}{n^2}$
$\Delta E_{n,n-1}=E_n-E_{n-1}=-\frac{1}{(n-1{)}^2}+\frac{1}{n^2}=\frac{2n-1}{n^2-n}$

This can be approximated to $\frac{2}{n}$ when $n$ is very large.
Thus, energy difference between consecutive levels decreases as $n$ increases.