Question

You use a microwave oven to heat your dinner. The frequency of the radiation is `2.37 times 10^9 s^-1`. What is the energy of one photon of this radiation?

Answer 1

`1.57 * 10^(-24)"J"`

Explanation:

The energy of a photon is actually directly proportional to its frequency as given by the Planck - Einstein relation

`color(blue)(ul(color(black)(E = h * nu)))`

Here

• `E` is the energy of the photon
• `h` is Planck's constant, equal to `6.626 * 10^(-34)"J s"`
• `nu` is the frequency of the photon

This basically means that photons of higher frequencies are more energetic than photons of lower frequencies.

Since you already know the frequency of the photon, all you have to do here is plug in your value into the above equation

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 2.37 * 10^(9)color(red)(cancel(color(black)("s"^(-1)))) = color(darkgreen)(ul(color(black)(1.57 * 10^(-24)"J")))`

The answer is rounded to three sig figs.