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#?

Question

Emilia Acosta · Accepted Answer

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

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.

Alice Andrews · Answer

undefined The wavelength of a photon can be found using the formula λ = hc/E, where h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and E is the photon's energy. Entering these values yields the following result: λ = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s) / (6.4 x 10^-19 J). This gives us the wavelength in meters, which we can then convert to nanometers (1 m = 1 x 10^9 nm).