Question

How can I calculate the wavelength from energy?

Answer 1

To calculate the wavelength, you need to know either the frequency or the energy of the radiation.

Wavelength from frequency:

For example, what is the wavelength of a radio wave with a frequency of

$590kHz$?

$f\lambda =c$

$\lambda =\frac{c}{f}=\frac{2.998\ast {10}^{8}m{s}^{-1}}{590\ast {10}^3{s}^{-1}}=508m$

Wavelength from energy

The formula is

$E=\frac{hc}{\lambda }$ or $\lambda =\frac{hc}{E}$, where $h$ is planck's constant.

For example, what is the wavelength of a photon that has an energy of

$3.36\ast {10}^{19}J$?

$\lambda =\frac{hc}{E}=\frac{6.626\ast {10}^{-34}J\cdot s\ast 2.998\ast {10}^{8}m{s}^{-1}}{3.36\ast {10}^{-19}J}=5.91\ast {10}^{-7}m=591nm$