# 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?

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:
$E = \frac{h c}{\lambda}$

Where $h$ is Planck's constant ($\cong 6.626 \times {10}^{-} 34$ Js)
And $c$ is the speed of light in vacuum ($\cong 2.9979 \times {10}^{8}$ m/s)
Thus $h c \cong 1.9864 \times {10}^{-} 25$ Jm

We can manipulate the previous equation to solve for wavelength:
$\lambda \cong \frac{h c}{E} = \frac{1.9864 \times {10}^{-} 25}{6.4 \times {10}^{-} 19}$
$\lambda \cong 0.310 \times {10}^{-} 6 = 310 \times {10}^{-} 9$ meters

Thus $\lambda \cong 310$ nm. One can confirm from other sources that this places the photon in the UV B wavelength range.