Convert wavenumber to energy in joules or eV, or energy back to wavenumber, and see the matching wavelength and frequency of the photon.
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Energy from Wavenumber Formula
The following equation is used to calculate the Energy from Wavenumber.
Variables:
- Where E is the energy (joules) per photon
- k is the spectroscopic wavenumber 1/ฮป in vacuum (mโ1), not angular wavenumber 2ฯ/ฮป; if given in cmโ1, convert using 1 cmโ1 = 100 mโ1
- h is Planck’s constant (6.62607015 ร 10โ34 Jยทs)
- c is the speed of light in vacuum (2.99792458 ร 108 m/s)
To calculate energy from wavenumber, multiply the wavenumber (in mโ1) by hยทc.
| Wavenumber (cmโปยน) | Energy (J) | Energy (eV) | Energy (kcal) |
|---|---|---|---|
| 10 | 1.986e-22 | 0.001240 | 4.748e-26 |
| 50 | 9.932e-22 | 0.006199 | 2.374e-25 |
| 100 | 1.986e-21 | 0.012398 | 4.748e-25 |
| 200 | 3.973e-21 | 0.024797 | 9.495e-25 |
| 400 | 7.946e-21 | 0.049594 | 1.899e-24 |
| 500 | 9.932e-21 | 0.061992 | 2.374e-24 |
| 750 | 1.490e-20 | 0.092988 | 3.561e-24 |
| 1000 | 1.986e-20 | 0.123984 | 4.748e-24 |
| 1500 | 2.980e-20 | 0.185976 | 7.122e-24 |
| 2000 | 3.973e-20 | 0.247968 | 9.495e-24 |
| 2500 | 4.966e-20 | 0.309960 | 1.187e-23 |
| 3000 | 5.959e-20 | 0.371953 | 1.424e-23 |
| 3300 | 6.555e-20 | 0.409148 | 1.567e-23 |
| 4000 | 7.946e-20 | 0.495937 | 1.899e-23 |
| 5000 | 9.932e-20 | 0.619921 | 2.374e-23 |
| 10000 | 1.986e-19 | 1.239842 | 4.748e-23 |
| 15000 | 2.980e-19 | 1.859763 | 7.122e-23 |
| 20000 | 3.973e-19 | 2.479684 | 9.495e-23 |
| 25000 | 4.966e-19 | 3.099605 | 1.187e-22 |
| 30000 | 5.959e-19 | 3.719526 | 1.424e-22 |
| Constants: h = 6.62607015ร10โปยณโด Jยทs; c = 2.99792458ร10โธ m/s; 1 eV = 1.602176634ร10โปยนโน J; 1 kcal = 4184 J. E (per photon) = hยทcยทwavenumber, with wavenumber in mโปยน (1 cmโปยน = 100 mโปยน). | |||
How to Calculate Energy from Wavenumber?
The following two example problems outline the steps and information needed in order to calculate the Energy from Wavenumber.
Example Problem #1:
- First, determine the wavenumber. In this example, the wavenumber is measured to be 1441 cmโ1.
- Finally, calculate the energy from wavenumber using the formula above:
E = h*c*k
Inserting the values from above and solving the equation with the inputted values gives:
E = (6.62607015 * 10-34) * (2.99792458 * 108) * (1441 * 100) = 2.862e-20 (joules)
Example Problem #2:
Using the same process as example problem 1, we first define the needed variables outlined by the formula. In this case, the values are provided as:
wavenumber = 123561 cmโ1
Entering these values into the formula or calculator above gives us:
E = (6.62607015 * 10-34) * (2.99792458 * 108) * (123561 * 100) = 2.454e-18 (joules)
