Question

What is the energy in electron volts of X-rays that have a frequency of `3.00 * 10^16` `Hz`?

Answer 1

`"124 eV"`

Explanation:

The first thing to do here is use the Planck - Einstein Relation to calculate the energy of an X-Ray photon that has a frequency of `3.00 * 10^(16)"Hz"`.

According to the Planck - Einstein Relation, the energy of a photon is proportional to its frequency

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

Here

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

Before plugging in your value for the frequency of the photon, don't forget to use the fact that `"1 Hz"` is equal to `"1 s"^(-1)`. You will thus have

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 3.00 * 10^(16)color(red)(cancel(color(black)("s"^(-1))))`

`E = 1.988 * 10^(-17)"J"`

Now, an electronvolt, `"eV"`, is simply the energy gained by a single electron when it's being accelerated through an electric potential difference of `"1 V"`.

`color(blue)(|bar(ul(color(white)(a/a)"1 eV" = 1.6022 * 10^(-19)"J"color(white)(a/a)|)))`

Use the definition of an electronvolt as a conversion factor to convert the energy of your photon from joules to eV

`1.988 * 10^(-17)color(red)(cancel(color(black)("J"))) * "1 eV"/(1.6022 * 10^(-19)color(red)(cancel(color(black)("J")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("124 eV")color(white)(a/a)|)))`

The answer is rounded to three sig figs.