Determine Energy of Mol of Photons of Light

• Wavelength is normally reported in nanometers (nm) and should be converted to meters for energy calculation purposes

What you'll need:

Convert (nm) to (m): Wavelength in (nm) X by 10 ^ -9

Speed of Light: 3.0 x 10^8 m/s

Planck's Constant:  6.63 x 10^-34

Avogadro's Number:  6.02 x 10^23

Energy of a Photon (in particles) = Speed of Light X Planck's Constant / Wavelength

Convert particles to mol -->  Avagadro's Number (6.02) X 10^23  X  Wavelength (in particles)

Convert g/mol to kJ/mol  = g/mol / 1,000


Example:

Determine the energy of 1.40 of photons for: 

Infrared radiation (1580 ) 

Convert Wavelength from (nm) to (m):  1580 nm X 10^-9 = 0.00000158 = 1.58 X 10 ^ -6 (m)

Energy of a Photon (in particles) = 3.0 X 10^8 * 6.63 X 10 ^ -34 / 1.58 X 10 ^ -6 = 0.0000000000000000001258860759493670886075949367088607594936708861 = 1.259 X 10 ^ -19

Convert particles to 1.40 mol = 1.259 X 10 ^ -19 * (6.02 X 10^23) * 1.40 = 106096.78481012658227848101265822784810126582280508 = 1.06 X 10^5 g/mol

Convert g/mol to kJ/mol = 1.06 X 10^5 / 1000 = 106 kJ

Sidenote (in the form of what you call a Red-flag): Instead of stupidly calculating the Speed of Light X Planck's Constant everysingle mother f'ing time (hello & hi, why am I doing this), let's just calculate that baby and put it on the shelf.

Speed of Light X Planck's Constant (a.k.a half of the equation, during step #2):

or 1.99 X 10^-25


Visible light (495 )

495 (nm) X 10^-9 = 4.95 * 10^-7 (m)

3.0 * 10^8 X 6.63 * 10^-34 / 4.95*10^-7 = 0.00000000000000000040181818181818181818
= 4.02 X 10^-19

4.02 * 10^-19 X (6.02 X 10^23) X 1.40 = 338652.36 or 3.39 X 10^5 g/mol

33880.56/1000 = 338.65 = 339

Ultraviolet radiation (155 )

155 (nm) X 10^-9 = 0.000000155 = 1.55 * 10^-7

 1.99 X 10^-25/1.55 *10^-7 = 0.0000000000000000012838709677419354839
= 1.28 * 10^-18

1.28 * 10^-18 X (6.02 X 10^23) X 1.40 = 1082046.45161290322583092 or 1.08 X 10^6 g/mol

1.08 X 10^6 / 1000 = 1082.04645161290322583092 = 1082