A moving hydrogen atom makes a head on collision with a stationary hydrogen atom. Before collision both atoms are in in ground state and after collision they move together. What is the minimum value of the kinetic energy of the moving hydrogen atom, such that one of the atoms reaches one of the excited state?

Options

A. `20.4eV`
B. `10.2eV`
C. `54.4eV`
D. `13.6eV`

Answer

A

Explanation

`K = (P^2) /(2m)`
in collision, momentum p remains constant.
`:. K prop (1)/(mass)`
After collision, mass has doubled. So kinetic
energy will remain `(K)/(2).` Hence,loss is also `(K)/(2)`
Now, `(K)/(2)` = minimum excitation energy required.
=10.2 eV
`rArr K = 20.4 eV`