The energy of an electron in the ground state ( $n=1$ ) for $\mathrm{He}^{+}$ion is $-x \mathrm{~J}$

Question

The energy of an electron in the ground state ( $n=1$ ) for $\mathrm{He}^{+}$ion is $-x \mathrm{~J}$, then that for an electron in $n=2$ state for $\mathrm{Be}^{3+}$ ion in J is

Professor PC Thomas Classes · Answer

(a) : $E_n=-R_{\mathrm{H}} \frac{Z^2}{n^2}$ For ground state $\mathrm{He}^{+}$ion, $Z=2, n=1$ \ $ E_1=-R_{\mathrm{H}} \frac{2^2}{1^2}=-4 R_{\mathrm{H}}=-x \mathrm{~J} $ For an electron in $n=2$ state for $\mathrm{Be}^{3+}$ ion $(Z=4)$, $ E_2=-R_{\mathrm{H}} \frac{4^2}{2^2}=-4 R_{\mathrm{H}}=-x \mathrm{~J} $