Question

A hydrogen-like an atom has its single electron orbiting around its stationary nucleus. The energy to excite the electron from the second Bohr orbit to the third Bohr orbit is $47.2eV$. The atomic number of this nucleus is ______.

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

The correct option is D 5

Energy for excitation from $2^{nd}$ to $3^{rd}$ orbit

$\Delta E=13.6\times Z^2\times [\frac{1}{(2{)}^2}-\frac{1}{(3{)}^2}]$ $eV$

$\therefore 47.2=13.6\times Z^2\times \frac{5}{9\times 4}$

$\therefore Z^2=24.98$

$\therefore Z\approx 5$