__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 Planck’s constant (h).

H = 6.63 x 10^{-34} Js

**E**_{photon} = 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 10^{8} m/s.

Hey, what’s 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 Planck’s equation to calculate
photon energy.

Example: Let’s 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 10^{9} nm) = *4.5 x
10*^{-7} m

Step 2: n = __3.00 x 10__^{8} m/s = *6.7 x 10*^{14}/s (or 6.7 x 10^{14 }s^{-1})

4.5
x 10^{-7} m

Step 3: E_{photon} = hn =
6.63 x 10^{-34} Js (6.7 x 10^{14}/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.