Question

Green light has a wavelength of 5200 A. How do you calculate the energy of one photon of green light?

Answer 1

`E = 3.8xx10^-19` `"J"`

Explanation:

We're asked to calculate the energy of one photon of a green light, given its wavelength of `5200` `"Å"`.

To do this, we can use the equation

`ul(E = (hc)/f`

where

• `E` is the energy of the photon (in joules)

• `h` is Planck's constant, equal to `6.626xx10^-34` `"J"•"s"`

• `c` is the speed of light in vacuum, `299792458` `"m/s"`

• `f` is the frequency of the photon (in meters)

We need to convert from ångströms to meters, using the conversion factor

`1` `"m"` `= 10^10` `"Å"`:

`5200cancel("Å")((1color(white)(l)"m")/(10^10cancel("Å"))) = color(red)(ul(5.2xx10^-7color(white)(l)"m"`

The energy of the photon is thus

`color(blue)(E) = ((6.626xx10^-34color(white)(l)"J"•cancel("s"))(299792458cancel("m/s")))/(color(red)(5.2xx10^-7cancel("m"))) = color(blue)(ulbar(|stackrel(" ")(" "3.8xx10^-19color(white)(l)"J"" ")|)`

rounded to `2` significant figures.