Question

An electron collides with a Hydrogen atom in its ground state and excites it to $n = 3$ state. The energy given to the Hydrogen atom in this inelastic collision (neglecting the recoil of Hydrogen atom) is

• A. 10.2 eV
• B. 12.1 eV
• C. 12.5 eV
• D. 13.6 eV

Answer 1

The Correct Option is B

According to the question,
Energy given to hydrogen atom $=$ Difference in energy level from
$n_{1}=1$ to $n_{2}=3$ states
$=13.6\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)=13.6\left(\frac{1}{1^{2}}-\frac{1}{3^{2}}\right)=13.6\left(1-\frac{1}{9}\right)$
$=13.6 \times \frac{8}{9}=12.08 \approx 12.1 eV$