Question

The wavelength of an EM wave is 800 nm. Calculate its frequency, angular frequency, wavenumber, wave vector amplitude, energy, and momentum.

Answer 1

Answer:

Given: Wavelength (λ) = 800 nm

Frequency $\nu=\frac{c}{\lambda} \Rightarrow \nu = \frac{3\times10^8}{800\times 10^{-9}} =3.75\times10^{14} Hz$

Angular frequency $\omega=2\pi \nu \Rightarrow \omega = 2\pi 3.75\times10^{14} = 23.55\times10^{14} rad/s$

Wavenumber, $k=\frac{2\pi}{\lambda} \Rightarrow k =\frac{2\pi}{800\times 10^{-9}}=7.85\times 10^6m^{-1}$

wave vector amplitude |k| = k = $7.85\times 10^6m^{-1}$

energy, $E = h \nu \Rightarrow E = 6.63\times 10^{-34}\times 3.75\times10^{14} = 24.86\times 10^{-20}J$

momentum, $p=\frac{h}{\lambda} = \frac{6.63\times 10^{-34}}{800\times 10^{-9}}= 8.28\times 10^{-28}Ns$