Question

Question #9754c

Answer 1

`3.3 * 10^(-17)"J"`

Explanation:

The idea here is that the energy of the photon is proportional to its frequency as shown by the Planck - Einstein relation

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

Here you have

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

Notice that the problem provides you with the period of the wave, `T`. As you know, the period of the wave is inversely proportional to its frequency

`color(purple)(|bar(ul(color(white)(a/a)color(black)(T = 1/nu)color(white)(a/a)|)))`

This means that the frequency of the wave will be

`nu = 1/T`

`nu = 1/(2 * 10^(-15)"s") = 5 * 10^(14)"s"^(-1)`

Plug this into the Planck - Einstein relation to get

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 5 * 10^(16)color(red)(cancel(color(black)("s"^(-1))))`

`E = color(green)(|bar(ul(color(white)(a/a)color(black)(3.3 * 10^(-17)"J")color(white)(a/a)|)))`

I'll leave the answer rounded to two sig figs.