Calculate the wavelength of a photon with energy 4.968 times 10 to the negative 19th joules using a value of 6.625 times 10 to the negative 34th joule seconds for Planck’s constant and a value of three times 10 to the eighth meters per second for the speed of light.
We can begin by recalling that the energy of a photon is equal to Planck’s constant times the speed of the photon divided by its wavelength. Rearranging this expression, we find that the wavelength, 𝜆, is equal to ℎ times 𝑐 over 𝐸.
And when we plug in the values given for these three terms, we see that the units of joules cancel out, as do the units of seconds, leaving us with units of meters. The result we calculate is four times 10 to the negative seventh meters. That’s the wavelength of the photon with the given amount of energy.