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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
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$12.1 \mathrm{eV}$
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
$=13.6\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=13.6\left(\frac{1}{1^2}-\frac{1}{3^2}\right)=13.6\left(1-\frac{1}{9}\right)$
$=13.6 \times \frac{8}{9}=12.08 \approx 12.1 \mathrm{eV}$
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