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?

1 Answer
Jul 12, 2016

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.