Question

What is the energy of a photon of light with a wavelength of 575 nm?

Answer 1

`3.46 * 10^(-19)"J"`

Explanation:

The energy of a photon is proportional to its frequency, as stated by the Planck - Einstein's equation

`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

Now, notice that you are given the wavelength of the photon, `lamda`. As you know, frequency and wavelength have an inverse relationship described by the equation

`color(blue)(lamda * nu =c)" "`, where

`c` - the speed of light in vacuum, approximately equal to `3 * 10^8"m s"^(-1)`

This means that the relationship between energy and wavelength looks like this

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

`E = h * c/(lamda)`

Another important thing to notice here is that the wavelength of the photon is given in nanometers, `"nm"`. You need to convert this to meters, the unit used for the value of the speed of light.

`E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * (3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-)))))/(575 * 10^(-9)color(red)(cancel(color(black)("m")))) = color(green)(3.46 * 10^(-19)"J")`