MCQ
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
    $-\,435.8\times 10^{-20}\,J$
  • $-\,271.9\times 10^{-20}\,J$
  • D
    $-\,108.9\times 10^{-20}\,J$

Answer

Correct option: C.
$-\,271.9\times 10^{-20}\,J$
c
Energy is directly proportional to the square of atomic number.

$\frac{E_{H}}{E_{H e+}}=\frac{Z_{H}^{2}}{Z_{H e+}^{2}}$

$E_{H}=\frac{Z_{H}^{2}}{Z_{H e+}^{2}} \times E_{H e+}$

$E_{H}=\frac{1^{2}}{2^{2}} \times-871.6 \times 10^{-20} J$

$E_{H}=\frac{1^{2}}{2^{2}} \times-871.6 \times 10^{-20} J$

$E_{H}=-217.9 \times 10^{-20} \mathrm{J}$

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