Question

Question #6f835

Answer 1

`4.1 * 10^(-26)"J"`

Explanation:

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

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

Notice that the problem provides you with the wavelength of the photon. In order to be able to calculate its energy, you will have to convert the given wavelength to frequency.

To do that, use the equation

`color(purple)(bar(ul(|color(white)(a/a)color(black)(lamda * nu = c)color(white)(a/a)|)))`

Here

`lamda` - the wavelength of the photon
`c` - the speed of light in a vacuum, usually given as `3 * 10^8"m s"^(-1)`

Rearrange this equation to solve for `nu`

`lamda * nu = c implies nu = c/(lamda)`

Plug in your values to find

`nu = (3 * 10^8 color(red)(cancel(color(black)("m"))) * "s"^(-1))/(4.8color(red)(cancel(color(black)("m")))) = 6.25 * 10^7"s"^(-1)`

Now all you have to do is plug this into the Planck - Einstein equation and calculate the energy of the photon

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 6.25 * 10^7color(red)(cancel(color(black)("s"^(-1)))) = color(green)(bar(ul(|color(white)(a/a)color(black)(4.1 * 10^(-26)"J")color(white)(a/a)|)))`

The answer is rounded to two sig figs.