Question

An electron with kinetic energy $EeV$ collides with a hydrogen atom in the ground state. The collision is observed to be elastic for

• A. $0<E<\infty$
• B. $0<E<10.2eV$
• C. $0<E<13.6eV$
• D. $0<E<3.4eV$

Answer 1

The correct option is B $0<E<10.2eV$

The cross section for elastic scattering of electrons of less than 10.2-eV energy by free hydrogen atoms has been measured. The experimental approach was similar to that used by Bederson, in that a dc electron beam crossed an atomic hydrogen beam, which was chopped at a low frequency, and the signal was derived from the electrons scattered by the particles in the neutral beam. The electrons scattered by the beam were identified by their signal's appearing at the modulation frequency and at a specified phase. Direct measurements of the ratio of cross sections of the hydrogen atom and the molecule were made, and absolute values for the atomic cross section were obtained from knowledge of the absolute molecular cross-section.

The experimental results agree with theory.

Energy of electron in ground state $=\mathrm{0.13.6}$

In 2nd energy level $=-3.4$

Total difference in energy level $=-10.2$

So kinetic energy is $=10.2$

So we know that in an elastic collision some amount of kinetic energy of electron transferred to the hydrogen atom.