Question

How much energy does a photon of frequency `6 * 10^12` Hz have?

Answer 1

`4 * 10^(-21)"J"`

Explanation:

The energy of a photon is actually directly proportional to its frequency as shown by the Planck - Einstein relation, which looks like this

`color(blue)(|bar(ul(color(white)(a/a)E = h * nu color(white)(a/a)|)))`

Here

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

As you can see, the energy of the photon increases as its frequency increases. Simply put, the higher the frequency, the more energetic the photon.

Now, the frequency of the photon is expressed in hertz, `"Hz"`. One hertz is defined as one cycle per second, which means that your photon completes `6 * 10^(12)` cycles per second, `"s"^(-1)`.

The frequency of the photon can thus be expressed as

`nu = 6 * 10^(12)"s"^(-1)`

Plug this into the Planck - Einstein relation to find the energy of the photon

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 6 * 10^(12)color(red)(cancel(color(black)("s"^(-1))))`

`E = color(green)(|bar(ul(color(white)(a/a)color(black)(4 * 10^(-21)"J")color(white)(a/a)|))) ->` rounded to one sig fig