Question

UV light is responsible for sun tanning. How do you find the wavelength (in nm) of an ultraviolet photon whose energy is `6.4 x 10^-19`?

Answer 1

The photon will have a wavelength of about `310` nm.

Explanation:

The energy of a photon is proportional to its wavelength and is given by the equation:
`E = (hc)/lambda`

Where `h` is Planck's constant (`~= 6.626xx10^-34` Js)
And `c` is the speed of light in vacuum (`~= 2.9979xx10^8` m/s)
Thus `hc ~= 1.9864xx10^-25` Jm

We can manipulate the previous equation to solve for wavelength:
`lambda ~= (hc)/E = (1.9864xx10^-25 )/ (6.4xx10^-19)`
`lambda ~= 0.310xx10^-6 = 310xx10^-9` meters

Thus `lambda ~= 310` nm. One can confirm from other sources that this places the photon in the UV B wavelength range.