If the bonding energy of the electron in a hydrogen atom is 13.6 eV , then energy required to remove…

If the bonding energy of the electron in a hydrogen atom is 13.6 eV , then energy required to remove electron from first excited state of $\mathrm{Li}^{2+}$ is
  1. 122.4 eV
  2. 3.4 eV
  3. 13.6 eV
  4. 30.6 eV

Solution

$B . E=13.6 \mathrm{eV}=-E_1 \Rightarrow E_1=-13.6 \mathrm{eV}$ For $\mathrm{Li}^{2+}, \mathrm{z}=3, \mathrm{n}_1=2, \mathrm{n}_2=\infty$ $\therefore \quad \Delta \mathrm{E}=\mathrm{E}_{\infty}-\mathrm{E}_2=0-\left(-13.6 \times \frac{\mathrm{Z}^2}{\mathrm{~n}_1^2}\right)$ $=13.6 \times \frac{(3)^2}{(2)^2}=30.6 \mathrm{eV}$

Asked in: AP EAMCET 2024 (18 May Shift 1)

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