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

For an elastic collision to take place, there must be no loss in the energy of electron. The hydrogen atom will absorb energy from the colliding electron only if it can go from ground state to first excited state, i.e., from n = 1 to n = 2 state. For this, hydrogen atom must absorb energy E2−E1=−3.4−(−13.6)=10.2eV So, if the election possesses energy less than 10.2 eV, it would never lose it and hence collision would be elastic.