Question

A single electron orbits around a stationary nucleus of charge $+Ze$, where $Z$ is a constant and $e$ is the magnitude of the electronic charge. It required $47.2eV$ to excite the electron from the second Bohr orbit to the third Bohr orbit.
Find the energy required to excite the electron from the third to the fourth Bohr orbit.

• A. $18eV$
• B. $16.53eV$
• C. $19eV$
• D. $21eV$

Answer 1

Answer: (B)

$16.53eV$

$\begin{array}{c}\Delta E=13.6(\frac{1}{n_1^2}-\frac{1}{n_2^2})z^2\\ \text{given}{n}_1=2,n_2=3\\ 47\cdot 2=13\cdot 6z^2(\frac{1}{2^2}-\frac{1}{3^2})\\ z^2=25\\ z=5\end{array}$

$\begin{array}{c}\text{now, putting}{n}_1=3,n_2=4\\ \Delta E=13.6\times 2^2\times (\frac{1}{3^2}-\frac{1}{4^2})\\ =13.6\times 25\times \frac{7}{16\times 9}\\ =16.53eV\end{array}$

$\text{Correct B}$