Q140 / 160 · TS EAMCET 2017 · Physics
An electron collides with a hydrogen atom in its grownd 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$10.2 \mathrm{eV}$
- Correct answerB$12.1 \mathrm{eV}$
- C$12.5 \mathrm{eV}$
- D$13.6 \mathrm{eV}$
Solution
According to the question,
Energy given to hydrogen atom $=$ Difference in energy level from $n_1=1$ to $n_2=3$ states
$=13.6\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=13.6\left(\frac{1}{1^2}-\frac{1}{3^2}\right)=13.6\left(1-\frac{1}{9}\right)$
$=13.6 \times \frac{8}{9}=12.08 \approx 12.1 \mathrm{eV}$
Energy given to hydrogen atom $=$ Difference in energy level from $n_1=1$ to $n_2=3$ states
$=13.6\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=13.6\left(\frac{1}{1^2}-\frac{1}{3^2}\right)=13.6\left(1-\frac{1}{9}\right)$
$=13.6 \times \frac{8}{9}=12.08 \approx 12.1 \mathrm{eV}$
Hence, the correct answer is option: 'B'.