The minimum excitation energy of an electron revolving in the first orbit of hydrogen is

The minimum excitation energy of an electron revolving in the first orbit of hydrogen is
  1. $3.4 \mathrm{eV}$
  2. $8.5 \mathrm{eV}$
  3. $10.2 \mathrm{eV}$
  4. $13.6 \mathrm{eV}$

Solution

Energy of electron in $\mathrm{n}^{\text {th }}$ orbit
$\mathrm{E}_{\mathrm{n}}=\frac{-13.6 \mathrm{eV}}{\mathrm{n}^2}$
Excitation energy of electron from $n=1$ to $n=2$
$\mathrm{E}=-13.6\left[\frac{1}{2^2}-\frac{1}{1}\right]=-13.6\left[\frac{1}{4}-\frac{1}{1}\right]=10^{-2} \mathrm{eV}$
So, Minimum excitation energy $=10.2 \mathrm{eV}$

Asked in: AP EAMCET 2023 (19 May Shift 1)

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