An electron and a photon each have a wavelength of $1.00\; nm$. Find

$(a)$ their momenta,

$(b)$ the energy of the photon, and

$(c)$ the kinetic energy of electron.

$(a)$ Momentum of electron

$p=h / \lambda$

$=6.63 \times 10^{-25} \,kg \,m / s$

Momentum of photon $p=h / \lambda$

$=6.63 \times 10^{-25}\, kg \,m / s$

$(b)$ Energy of photon $E=m c^{2} \ldots \ldots(1)$

Now, $\lambda=h / m c$

$O r m=h / c \lambda$

Substituting value of $m$ in eq. $(1)$

$E=h c / \lambda$

$=1.24\, keV$

$(c)$ Kinetic energy of electron $K = p ^{2} / 2 \,m$

$=2.41 \times 10^{-19}\, J$

$=1.51\, eV$