Question

A H-atom moving with speed $v$ makes a head on collision with a H-atom at rest. Both atoms are in ground state. The minimum value of velocity $v$ for which one of atom may excite is

• A. $1.89\times {10}^{6}m/s$
• B. $8.79\times {10}^{6}m/s$
• C. $7.25\times {10}^{6}m/s$
• D. $13.6\times {10}^{6}m/s$

Answer 1

The correct option is A $1.89\times {10}^{6}m/s$

In ground state, energy $=-13.6eV.$
Energy in just next higher energy state $=-3.4eV.$
Minimum energy needed for transition $=10.2eV$
This minimum energy is provided by elastic head on collision with moving electron,
$\Rightarrow \frac{1}{2}\times m{v}^2=10.2eV$
$\Rightarrow \frac{1}{2}\times 9.1\times {10}^{-31}{v}^2=10.2\times 1.6\times {10}^{-19}$
$\Rightarrow V^2=\frac{10.2\times 2\times 1.6\times {10}^{-19-31}}{1.67}$
$\Rightarrow V^2=3.5868\times {10}^{12}$
$\Rightarrow V=1.89\times {10}^{6}m/s$