First slide

Hydrogen -like ion

Question

If first excitation potential of hydrogen – like atom is V electron volt, then the ionization energy of this atom will be

Moderate

A

V electron volt
B

3V/4 electron volt
C

4V/3 electron volt
D

cannot be calculated by given information

Solution

$\begin{aligned} First excitation energy = R h c (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = R h c (\frac{3}{4}) \\ ∴ \frac{3}{4} R h c = V e v \\ ∴ R h c = \frac{4}{3} V e v \end{aligned}$

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