
According to the above diagram, the difference in energy between the two states is given by
ΔE==−3.4eV−(−13.6eV)10.2eV
The formula to calculate the recoil speed is given by
v=mcΔE...(1)
From equation (1), it follows that
v===1.6×10−27kg×3×108ms−110.2eV×1eV1.6×10−19J3.4ms−1517ms−1
Therefore, x=17.