Question

The energy of the electron in 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. $-435\times {10}^{-20}J$
• C. $-217.9\times {10}^{-20}J$
• D. $-108.9\times {10}^{-20}J$

Answer 1

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

Energy is directly proportional to the square of atomic number.

$\frac{E_H}{E_{He+}}=\frac{Z_H^2}{Z_{He+}^2}$
$E_H=\frac{Z_H^2}{Z_{He+}^2}\times E_{He+}$
$E_H=\frac{1^2}{2^2}\times -871.6\times {10}^{-20}J$
$E_H=\frac{1^2}{2^2}\times -871.6\times {10}^{-20}J$
$E_H=-217.9\times {10}^{-20}J$