Question

An electron revolves round a nucleus of charge $+Ze.$ If the energy required to excite the electron from second to third Bohr orbit is $47.2eV$, then the energy required to excite the electron from $n=3$ to $n=4$ state will be

• A. $16.53eV$
• B. $13.6eV$
• C. $1.51eV$
• D. None of the above

Answer 1

The correct option is A $16.53eV$

Energy $E=\frac{-13.6Z^2}{n^2}eV$

$E_2-E_1=constant(\frac{1}{2^2}-\frac{1}{3^2})=47.2$
$\Rightarrow E_2-E_1=constant\times \frac{5}{36}=47.2$
$\Rightarrow constant=47.2\times \frac{36}{5}$
$E_3-E_4=constant(\frac{1}{3^2}-\frac{1}{4^2})=constant\times \frac{7}{144}$

Substituting the constant:
$E_3-E_4=47.2\times \frac{36}{5}\times \frac{7}{144}=16.52$