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(A) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = -13.6 \frac{Z^2}{n^2} \ eV$. For a hydrogen atom $(Z=1)

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Decreases

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(A) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = -13.6 \frac{Z^2}{n^2} \ eV$. For a hydrogen atom $(Z=1)$,the energy difference between two adjacent levels $n$ and $n+1$ is $\Delta E = E_{n+1} - E_n = 13.6 \left( \frac{1}{n^2} - \frac{1}{(n+1)^2} \right) \ eV$. As $n$ increases,the term $\frac{1}{n^2}$ decreases rapidly,and the difference between $\frac{1}{n^2}$ and $\frac{1}{(n+1)^2}$ also decreases. Therefore,the energy difference $\Delta E$ decreases as the Principal Quantum number $n$ increases.

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

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