📝 Exercise

What is the momentum and energy of a photon with angular wavenumber \(k=10^8 \text{m}^{-1}\)? Give your answer in SI units.

We can start with the equation for the momentum, which is easy:

\[ p = \hbar k \]

The equation for the energy can deduced directly as \(E = pc\), but if you forgot this, then,

\[ E = h \nu = \frac{hc}{\lambda} = p c \]

using the Planck relation (first equality) and the De Broglie relation (last equality).

import scipy
from scipy import constants

p_from_k = constants.hbar * 1e8
E_from_k = constants.c * p_from_k

print("The momentum of a photon with an angular wavenumber of 1e7 1/m is {0:.3e} m kg/s.".format(p_from_k))
print("The energy of a photon with an angular wavenumber of 1e7 1/m is {0:.3e} J.".format(E_from_k))

The momentum of a photon with an angular wavenumber of 1e7 1/m is 1.055e-26 m kg/s.
The energy of a photon with an angular wavenumber of 1e7 1/m is 3.162e-18 J.