Did you know electron can pass through the proton in a hydrogen atom?

In school, we learn about the energy levels of the electron in a hydrogen atom but it is never explicitly mentioned that the electron can pass through the proton in the nucleus of the atom.

Why is this important? Well…it is important because we can measure the size of the proton by measuring the time electron spends inside the proton. The larger the proton, the more time the electron spends inside it.

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“The 2S and 2P states of hydrogen show where the electron could be found at any given time. These images show the possible locations of the electron in each state; the proton, unmarked, is at the center of each image. In the 2S state, the electron overlaps the proton, and for a non-zero amount of time, the electron is inside of the proton itself. In the 2P state, the electron and the proton never overlap.” – reference

The energy difference between the 2S and 2P states is known as the Lamb shift. This energy difference could not be predicted by the Schrodinger’s equation, it could not be predicted by the Dirac equation either.  When it was first measured it became clear that vacuum fluctuations exist. This was the beginning of the rise of the theory of Quantum Electrodynamics in particular and the QFT (Quantum Field Theory) in general. You can read the Nobel lecture Willis E. Lamb gave in 1955 to learn about his revolutionary experiment. In his Nobel lecture he reminds us that:

In 1885, Balmer found that the wavelengths of fourteen lines of the hydrogen spectrum were given by a simple equation. In 1887, Michelson and Morley discovered a fine structure of some of these lines. The quantum theory was founded by Planck in 1900, and in 1913 Bohr gave rules of quantization which permitted a derivation of Balmer’s formula. Sommerfeld showed in 1916 that the fine structure of Bohr’s energy levels was caused by relativistic corrections. In 1924, De Broglie attributed wave properties to the electron and soon a quantum mechanics of the hydrogen atom emerged from the hands of Heisenberg, Born, and Schroedinger. Spin and magnetic moment of the electron were suggested by Uhlenbeck and Goudsmit in1925, and their dynamical equations were worked out by Thomas a year later. In 1928, Dirac discovered an equation which described an electron with wave properties, charge, spin, magnetic moment and a mass depending on velocity as required by relativity theory. The energy levels of hydrogen were given by Dirac’s theory with high precision.”

To repeat for emphasis, Dirac’s theory predicted that 2S and 2P states would have the same energy. When the difference (Lamb shift) was found it was revolutionary.

Measuring the Lamb shift is extremely difficult. Natalie Wolchover tells the story of modern experiments on the Lamb shift in her article titled “Physicists Finally Nail the Proton’s Size, and Hope Dies“. These modern experiments deduce the size of the proton by measuring the Lamb shift.

In the 2S state the electron spends time inside the proton which makes the attraction between the proton and the electron weaker because of partial charge cancelation.  Remember, electron carries -1 unit of electric charge and proton carries +1 unit of electric charge. The bigger the proton the longer the electron will stay inside the proton and the weaker the bond will be. This is one of the factors that contribute to the energy difference between the 2S and the 2P states.

Finally, I think that the best explanation of the Lamb shift is given by this page at HyperPhysics.

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