We have to calculate the energy of one photon in a microwave radiation of wavelength 12.2 cm.

Microwaves are a part of the electromagnetic spectrum.

The relation between the speed, wavelength and frequency of electromagnetic waves is:

$\overline{){\mathrm{c}}{}{=}{}{\mathrm{\lambda \nu}}}$

We can rearrange this equation to isolate frequency (ν).

$\overline{){\mathrm{\nu}}{}{=}{}\frac{\mathrm{c}}{\mathrm{\lambda}}}$

The energy of a photon of electromagnetic radiation is given by:

$\overline{){\mathrm{E}}{}{=}{}{\mathrm{h\nu}}}$

We can replace the frequency (ν) in this equation:

$\overline{){\mathrm{E}}{}{=}{}\frac{\mathrm{hc}}{\mathrm{\lambda}}}$

h = Planck’s constant = 6.626x10^{-34} J·s.

c = speed of light = 3.0x10^{8} m/s

Microwave ovens emit microwave energy with a wavelength of 12.2 cm. What is the energy of exactly one photon of this microwave radiation?

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