Question

An electron with kinetic energy E collides with a hydrogen atom in the ground state. The collision will be elastic.

• A. for all values of E.
• B. for $E<10.2$ eV.
• C. for $10.2$ eV $<$ E $<13.6$ eV only.
• D. for $0<$ E $<3.4$ eV only.

Answer 1

The correct option is C for $10.2$ eV $<$ E $<13.6$ eV only.

$\begin{array}{c}\text{Energy}=E\\ \text{Energy at ground}\text{State for hydrogen like atom}=-13.6\frac{z^2}{n^2}=V\\ \text{For hydrogen atom,}z=1\\ n=1\end{array}$

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

$\text{for 2nd shell}$

$\begin{array}{cc}E& =-13.6\times (\frac{1}{1^2}-\frac{1}{2^2})\\ & =-10.2eV\end{array}$

$10.2<E<13.6$

$\therefore \text{Opion C is correct}$