Question

A hydrogen atom moving with velocity $u$ collides inelastically with another hydrogen atom at rest. Both the atoms are in the ground state before collision. The minimum value of $u$,so that one of the atoms get excited, will be

• A. $3.12\times {10}^{6}m/s$
• B. $9.36\times {10}^{5}m/s$
• C. $6.24\times {10}^{4}m/s$
• D. $5\times {10}^{3}m/s$

Answer 1

Answer: (C)

$6.24\times {10}^{4}m/s$

Both the atoms move together with velocity $v$ after collision.

From conservation of momentum,

$mu=\left(2m\right)v$

$⟹v=\frac{u}{2}$

For the minimum value of $u$, the atom gets excited to the nearest state, i.e., $1\to 2$.

From conservation of energy,

$\frac{1}{2}m{u}^2=\frac{1}{2}\left(2m\right)v^2+10.2eV$

$⟹\frac{1}{4}m{u}^2=10.2eV$

$⟹u=6.24\times {10}^{4}m/s$