# Energy levels in hydrogen

If an electron from a low level is given energy it will be raised to a higher, or excited, level. This can be done electrically, by heat, by collision with another atom, by radiation or by a free electron hitting the atom. However the electron in the atom will only be excited if the energy of the incoming quantum of energy in whatever form is exactly the same as the difference in energy between the two levels.

When an electron falls from one level to another energy is emitted in the form of a quantum of radiation. The energy of this quantum and therefore its frequency and wavelength is determined by the difference in energy between the two levels.

Example problem
Calculate the frequency and wavelength of a quantum of radiation emitted when an electron in level 4 falls to level 2. Using the data in the table on page:
Energy of level 4 = - 1.36 x 10-19 J
Energy of level 2 = - 5.42 x 10-19 J
Energy difference (E) = + 4.06 x 10-19 J

Therefore frequency = E/h = 4.06 x 10-34/6.63 x 10-34 = 6.12 x 1014
Wavelength = c/f = 3 x 108/6.12 x 1014 = 4.9 x 10-7 m = 490 nm
This is in the deep blue to violet end of the visible spectrum.

N.B notice that joules have been used and not electron volts.

### schoolphysics: Emission of radiation animation

To see an animation of the emission of radiation from an atom please click on the animation link.

## Energy levels and transitions in hydrogen

 Level Energy (eV) Energy x10-19(J) Transition Energy (ev) Frequency(Hz) x1014 Wavelength (nm) ∞ 0 0 ∞ to 1 13.6 32.9 91 6 -0.38 -0.61 4 to 1 12.75 30.8 97.5 5 -0.54 -0.87 3 to 1 12.09 29.25 103 4 -0.85 -1.36 2 to 1 10.2 24.61 122 3 -1.51 -2.42 ∞ to 2 3.40 8.21 366 2 -5.42 -3.40 5 to 2 2.86 6.90 435 1 -13.60 -21.8 4 to 2 2.55 6.15 488 3 to 2 1.89 4.56 658 ∞ to 3 1.51 3.64 823 5 to 3 0.97 2.34 1281 4 to 3 0.66 1.59 1884 6 to 4 0.47 1.13 2644 5 to 4 0.31 74.8 4010 6 to 5 0.16 0.386 7769

You should be able to see from the above table that the only lines in the hydrogen spectrum visible to the human eye are those due to transistions from level 5 to level 2, from level 4 to level 2 and from level 3 to level 2 (wavelengths of 435 nm, 488 nm and 658 nm respectively)

A VERSION IN WORD IS AVAILABLE ON THE SCHOOLPHYSICS USB

© Keith Gibbs 2020