Question

A photon has a frequency of `2.68 * 10^6` Hz. What is its energy?

Answer 1

`1.78 * 10^(-27)"J"`

Explanation:

As you know, the energy of a photon is directly proportional to its frequency.

This relationship between energy and frequency is established by the Planck - Einstein equation, which looks like this

`color(blue)(E = h * nu)" "`, where

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

Notice that the frequency of the photon is given to you in hertz, `"Hz"`. As you know, one hertz, which denotes one cycle per second, is equivalent to

`"1 Hz" = "1 s"^(-1)`

Plug in the value you have and solve for `E` to get

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 2.68 * 10^6color(red)(cancel(color(black)("s"^(-1))))`

`E = 1.7758 * 10^(-27)"J"`

Rounded to three sig figs, the answer will be

`E = color(green)(1.78 * 10^(-27)"J")`