Question

The energy of electron in first orbit of He' is $-871.6\times {10}^{-20}J$. The energy of electron in the first orbit of H is :

• A. $-871.6\times {10}^{-20}$
• B. $-435.8\times {10}^{-20}$
• C. $-217.9\times {10}^{-20}$
• D. $-108.9\times {10}^{-20}$

Answer 1

Answer: (C)

$-217.9\times {10}^{-20}$

Total energy of an electron $E_n$ in the $n^{th}$ orbit is proportional to the square of the atomic number $Z$ and inversely proportional to the square of the principle quantum number (orbit) of electron and the nucleus.
$E_n\propto \frac{Z^2}{n^2}$
Therefore
$\frac{E_{H_1}}{E_{H{e}_1}}=\frac{Z_H^2}{Z_{He}^2}$
For, $Z_H=1$, $Z_{He}=2$ and $n=1$, and $E_{H{e}_1}=-871.6\times {10}^{-20}J$.
$\frac{E_{H_1}}{E_{H{e}_1}}=\frac{Z_H^2}{Z_{He}^2}=\frac{1}{4}$
$E_{H_1}=\frac{1}{4}\times -871.6\times {10}^{-20}J=-217.9\times {10}^{-20}J$
Option 'C' is correct.