In a hydrogen like ion, the energy difference between the excitation energy state and ground is 108.8 eV. The atomic number of the ion is [2025]

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Solution

Q.
In a hydrogen like ion, the energy difference between the $2^{nd}$ excitation energy state and ground is 108.8 eV. The atomic number of the ion is [2025]

1 4

2 2

3 1

4 3

Ans.
(4)

$△ E = 13.6 Z^{2} [\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}]$

$13.6 Z^{2} [\frac{1}{1} - \frac{1}{9}] = 108.8$

$\frac{13.6 \times 8}{9} (Z^{2}) = 108.8 \Rightarrow Z = 3$

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