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# Can electron reside inside the nucleus of an atom ?

I think we all  know about the Rutherford model of an atom. Yeah,  I am telling about that famous experiment performed by Ernest Rutherford in 1911. Rutherford overturned J.J. Thomson’s so called “Plum-Pudding model” with his well-known gold foil experiment (also known as α-particle scattering experiment since he used -particle for the experiment)  in which he demonstrated that the atom has a tiny, massive nucleus surrounded by a cloud of orbiting electrons.

The key points of that experiment are:

• The electron cloud of the atom do not influence alpha particle scattering.
• Much of an atom’s charge (specifically, its positive charge) is concentrated in a relatively tiny volume at the center of the atom, known today as the nucleus. The magnitude of this charge is proportional to (up to a charge number that can be approximately half of) the atom’s atomic mass – the remaining mass is now known to be mostly attributed to neutrons (which are neutral) .This concentrated central mass and charge is responsible for deflecting alpha particles.
• The mass of heavy atoms such as gold is mostly concentrated in the central charge region, since calculations show it is not deflected or moved by the high speed alpha particles, which have very high momentum in comparison to electrons, but not with regard to a heavy atom as a whole.

Now let’s come to Beta decay. In nuclear physics, beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted from the nucleus of an atom. Beta decay is a process which allows the atom to obtain the optimal ratio of protons and neutrons.

But here, the question arises. If the nucleus consists of Protons and Neutrons; then how is it possible for a beta particle (I mean electron) to be emitted from the nucleus during the radioactive decay !!! Does nucleus contain electron(s) also ?

Well,  scientists have given us a very beautiful explanation as mentioned below:

An unstable atomic nucleus with an excess of neutrons may undergo β- decay, where a neutron is converted into a proton, an electron and an electron-type antineutrino (the antiparticle of the neutrino):

n --> p + e- + νe-

yessssss… this theory looks quite impressive.  But can we prove by some other way that electron can not reside inside the nucleus ? Do we have any other theory to prove that ??

The answer is YES. We have…

Here comes the Heisenberg’s Uncertainty principle…  The uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be known simultaneously. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.

Mathematically,

where is the reduced Planck constant.

Now, we consider a nucleus of size 10^(-14) m.    Taking Δx to be the half-width of the confinement length, we have

Δp >= ℏ/(2Δx)

when we put the values of ℏ=  1.055* 10^(-34) J/s

then we will get  Δp >= 2.0 * 10^7    eV/c

This means that measurments of the components of momentum of electrons trapped inside a nucleus would range from less than -20 MeV/c  to greater than +20 MeV/c and that some electrons would have momentum at least as large as 20 MeV/c. Because this appears to be a large momentum, to be safe we calculate the electron’s energy relativistically ,

E^2= p^2 c^2 + (mc^2)^2

=(20 MeV/c)^2 c^2 + (0.511 MeV)^2

= 400 (MeV)^2

or, E >= 20 MeV

Since electrons emitted in radioactive decay(beta decay) have energies much lesser than 20MeV (about 1 MeV or less); we can conclude that electrons observed in beta decay do not come from within the nucleus but are actually created at the instant of decay.

So, after a long discussion I hope we have arrived at the answer of the very first question “Can electron reside inside the nucleus of an atom?”

Written by Dhiraj Sarmah.

References: Concepts of Modern Physics by A. Beiser.

# 1 COMMENT

1. good post, i have been looking for it

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