Question

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

• A. 2
• B. 5
• C. 3
• D. 4

Answer 1

The correct option is B 5

Excitation energy of hydrogen like atom for $n_2\to n_1$
$\Delta E=13.6Z^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})eV\Rightarrow 47.2=13.6Z^2(\frac{1}{2^2}-\frac{1}{3^2})=13.6\times \frac{5}{36}{Z}^2\Rightarrow Z^2=\frac{47.2\times 36}{13.6\times 5}=24.98\approx 25\Rightarrow Z=5$