Question

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

• A. 2
• B. 5
• C. 3
• D. 4

Answer 1

Answer: (B)

5

Answer 2

Excitation energy of hydrogen like atom for $n_{2} \rightarrow n_{1}$

$\Delta E = 13.6Z^{2}\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)eV$

⇒ $47.2 = 13.6Z^{2}\left( \frac{1}{2^{2}} - \frac{1}{3^{2}} \right) = 13.6 \times \frac{5}{36}Z^{2}$

⇒ $Z^{2} = \frac{47.2 \times 36}{13.6 \times 5} = 24.98\widetilde{-}25$

⇒ Z = 5