Question

A single electron orbit around a stationary nucleus of charge +Ze where Z is the atomic number and 'e' is the magnitude of the electric charge. The hydrogen-like species required 47.2eV to excite the electron from the second Bohr orbit to the third Bohr orbit. The value of Z is:

• A. 5
• B. 3
• C. 2
• D. 4

Answer 1

Answer: (A)

5

$\Delta E=\frac{hc}{\lambda }=R{Z}^{2}hc[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
For transition from $2\to 3$
$47.2\times 1.6\times {10}^{-19}=1.09678\times {10}^7\times Z^2\times 6.62\times {10}^{-34}\times 3\times {10}^8\times [\frac{1}{2^2}-\frac{1}{3^2}]$
$\Rightarrow Z=5$