Question

Question #1e68a

Answer 1

`4 * 10^(-19)` `"J"`

Explanation:

The thing to remember here is that the energy of a photon is directly proportional to its frequency and, consequently, inversely proportional to its wavelength.

This relation is described by the Planck - Einstein relation, which looks like this

`E =h * c/(lamda)`

Here

• `E` is the energy of the photon
• `h` is Planck's constant, equal to `6.626 * 10^(-34)"J s"`
• `c` is the speed of light in a vacuum, usually given as `3 * 10^8"m s"^(-1)`
• `lamda` is the wavelength of the wave

Now, notice that the speed of light in a vacuum is expressed in meters per second. This tells you that you need to convert the wavelength of the photon from nanometers to meters by using the fact that

`"1 m" = 10^9color(white)(.)"nm"`

Plug in the value you have for the wavelength of the photon and solve for `E`

`E = 6.626 * 10^(-34)color(white)(.)"J" color(red)(cancel(color(black)("s"))) * (3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(500 * 10^(-9)color(red)(cancel(color(black)("m"))))`

`E = color(darkgreen)(ul(color(black)(4 * 10^(-19)color(white)(.)"J"`

The answer is rounded to one significant figure, the number of sig figs you have for the wavelength of the photon.