Calculating Photon Energy

For lab, you need to calculate the photon energies for the bright lines of Hydrogen only!† The hydrogen spectrum shows 4 bright lines: red, yellow (sometime rather faint), turquoise and purple.

Calculating the energy of a photon requires the light frequency (n) and Planckís constant (h).

H = 6.63 x 10-34 Js

Ephoton = hn

Problem: The spectroscopes give us data in terms of wavelength (l) in nanometers.

So, we need to use math to calculate the frequency from the wavelength.

c = ln, where c = the speed of light in a vacuum = 3.00 x 108 m/s.

Hey, whatís nu?† n = c/l

Problem: The spectroscope gives us wavelength in nm, but speed of light is in m.

Step 1: convert nm wavelengths to m.

Step 2: use n = c/l to convert wavelength to frequency.

Step 3: use Planckís equation to calculate photon energy.

Example: Letís say you observed a purple line at 4.5 in the spectroscope.† 4.5 x 100 = 450 nm.

Step 1: 450 nm x (1m/†1 x 109 nm)††† = 4.5 x 10-7 m

Step 2:† n = 3.00 x 108 m/s†††† =†† 6.7 x 1014/s† (or 6.7 x 1014 s-1)

††††††††††††††††††4.5 x 10-7 m

Step 3: Ephoton = hn = 6.63 x 10-34 Js (6.7 x 1014/s) = 4.4 x 10-19 J.

So, the energy of a single purple photon of 450 nm wavelength is

4.4 x 10-19 Joules.

Show a set of sample calculations in your lab, and then calculate the photon for the other 3 bright lines of hydrogen.