Ans : (a)
$ \lambda = 10^{-15}m$
Rest mass energy of electron: $m_oc^2 = 0.511\: MeV$
$= 0.511 \times 10^6 \times 1.6 \times 10^{-19}$
$= 0.8176 \times 10^{-13} J$
Momentum of a proton, $p = \large\frac{h}{\lambda}$
$= \large\frac{6.6 \times 10^{-34}}{ 10^{-15}} = 6.6 \times 10^{-19} kg m/s$
Relativistic relation for energy (E) is :
$E^2 = p^2c^2 + m^2_oc^4$
$= (6.6 \times 10^{-19} \times 3 \times 10^8 )^2 + (0.8176 \times 10^{-13} )^2$
$= 392.04 \times 10^{-22} + 0.6685 \times 10^{-26}$
$≈ 392.04 \times 10^{-22}$
So, $E = \large\frac{1.98 \times 10^{-10} J}{ 1.6 \times 10^{-19}} = 1.24 \times 10^9 \: eV = 1.24\: BeV$