Question

A electron of the kinetic energy 10 eV collides with a hydrogen atom is 1st excited state . Assuming loss of kinetic energy in the collision to be quantized. Which of the following statement is correct ?
(a) The collision may be perfectly inelastic
(b) The collision may be inelastic

Answer 1

Energy of first excited state of Hydrogen is $(x=2)$

$E_1=-13.6\times \frac{z^2}{x^2}=\frac{-13.6\times 1^2}{x^2}=-13.4eV$

Energy difference between states respect to $x=2$ is given as :-

The electron has $KE=10eV$ which can transfer it to that $H-atom$, but maximum energy transferred can be $=10ev$ as per conservation of Energy.

Now, only transition $x=2$ to $x=3,4,\mathrm{5.....}\infty$ can happen to their energy difference is $<10eV$.

Due to the energy transfer from the electron, Its Kinetic energy will reduce $(\Delta k<0)$ then it will be an inelastic collision.

However, for more cases, all energy of electrons is not last, thus the collision will never be perfectly Inelastic.