Question

An electron with kinetic energy $EeV$ collides with a hydrogen atom in the ground state. The collision is observed to be elastic for

• A. $0\text{<}E\text{<}\infty$
• B. $0\text{<}E\text{<}10.2eV$
• C. $0\text{<}E\text{<}13.6eV$
• D. $0\text{<}E\text{<}3.4eV$

Answer 1

Answer: (B)

$0\text{<}E\text{<}10.2eV$

Electron collision elastic if no energy is absorbed for transition of electron
Min energy required for transition = $n=1\to n=2$
Attached concept
$E=13.6(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
$E_{min}=13.6(1-\frac{1}{2^2})$
$E_{min}=10.2eV$
Hence elastic collision if $E<10.2eV$