With increasing Principal Quantum number, the energy difference between adjacent energy levels in H-atom

Therefore the energy difference between ${\mathrm{n}}_1\&{\mathrm{n}}_2$  energy level,

Energy formula for the hydrogen atom is :-

$∆\mathrm{E}={\mathrm{E}}_{{\mathrm{n}}_2}-{\mathrm{E}}_{{\mathrm{n}}_1}=13.6{\mathrm{Z}}^2\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$

$∆\mathrm{E}\propto \mathrm{ }\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$

${\mathrm{n}}_1\&{\mathrm{n}}_2=$ principle quantum Number

$\because ∆\mathrm{E}\propto \mathrm{ }\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$ so when ${\mathrm{n}}_1\&{\mathrm{n}}_2$  increases

$∆\mathrm{E}$decreases.

Change in energy is inversely proportional to the increase in the principle quantum number.

Hence, with increasing Principal Quantum number, the energy difference between adjacent energy levels in $\mathrm{H}-$atom decreases.