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

Answer:

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.