Question

The energy of the first orbit of ${He}^{+}$ is $-871.6\times {10}^{-20}J$.The energy of the electron in the first orbit of hydrogen would be:

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

Answer 1

The correct option is C $-217.9\times {10}^{-20}J$

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

As we know that,

$E=2.18\times {10}^{-18}\left(\frac{Z^2}{n^2}\right)$

Since n is same,

$E\propto Z^2$

$\therefore \frac{E_{He}}{E_H}=\frac{{Z_{He}}^2}{{Z_H}^2}$

$\Rightarrow \frac{871.6\times {10}^{-20}}{E_H}=\frac{2^2}{1^2}$

$\Rightarrow E_H=\frac{871.6\times {10}^{-20}}{4}=-217.9\times {10}^{-20}J$