Question

A single electron orbits a stationary nucleus of charge $+$Ze, where Z is a constant. It requires $47.2$ eV to excite electron from second Bohr orbit to third Bohr orbit, find the value of Z.

• A. $1$
• B. $3$
• C. $5$
• D. $4$

Answer 1

The correct option is C $5$

Let us consider the problem:

$n_1=2\to n_2=3:\epsilon =47.2eV$

We have

$\epsilon =13.6z^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)eV$

Implies that

$47.2=13.6z^2\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$

Hence the answer is $z=5$.