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.
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 $K = p ^{2} / 2 \,m$
$=2.41 \times 10^{-19}\, J$
$=1.51\, eV$
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