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Composition of Nucleus

After the discovery of nucleus in 1911 by Ernest Rutherford, several hypothesis were given to explain the composition of nucleus. The most prominent among them were :-

Proton-Electron hypothesis
Proton-Neutron hypothesis

Proton-Electron hypothesis (1930)

(Composition of Nucleus)

The study of radioactive disintegration indicated the emission of alpha, beta(fast moving electrons) and gamma rays to be of nuclear origin. So it is quite logical to assume that nuclei contain electrons.

The electrostatic potential of two protons in the nucleus…

$\displaystyle V=\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}=\left[ 9\times {{10}^{9}}\times \frac{{{(1.6\times {{10}^{-19}})}^{2}}}{{{10}^{-15}}} \right]\times \frac{1}{1.6\times {{10}^{-19}}}eV$

$\displaystyle \Rightarrow V=1.4\times {{10}^{6}}eV=1.4MeV$

That’s a very large repulsive potential. Now imagine the repulsive Coulomb energy for several protons packed tightly into a nucleus. We have a major problem here for the stability of nucleus.

So a logical guess for the stability of nucleus is that, there must be some role of electrons in the composition of nucleus, which reduce the large Coulomb repulsion.

Neutron was not discovered at that time(discovered by Chadwick in 1932) and since atom as a whole is electrically neutral, so it was assumed that about half of an atom’s electrons are contained within the nucleus and rest of the electrons revolve around the nucleus.

According to this Proton-Electron hypothesis, protons and electron were considered as the building blocks of the nucleus. It was assumed that for an atom _ZX^A, there are A protons and (A-Z) electrons within the nucleus and since an atom, as a whole, is neutral, so Z electrons revolve around the nucleus in circular orbits.

Failure of Proton-Electron hypothesis

(Composition of Nucleus)

Reason 1 :- Energy of electron inside the nucleus

Suppose an electron exists inside the nucleus of radius 5 × 10^-15m. So uncertainty in the measurement of position of electron, i.e., Δx = 2 × 5 × 10^-15m = 10^-14 m

Using Heisenberg’s uncertainty principle,

Δx × Δp ≈ h/4π

We get,

$\displaystyle \Delta p\approx \frac{h}{4\pi \times \Delta x}\approx \frac{6.63\times {{10}^{-34}}}{4\pi \times {{10}^{-14}}}\approx 5.28\times {{10}^{-21}}Kgm/s$

Now let us find out energy of electron having uncertainty in the measurement of momentum, Δp ≈ 5.28 × 10^-21 Kg m/s

So using E = p²/2m, we get…

$\displaystyle E=\frac{{{p}^{2}}}{2m}=\left[ \frac{{{(5.28\times {{10}^{-21}})}^{2}}}{2\times (9.1\times {{10}^{-31}})} \right]\times \frac{1}{1.6\times {{10}^{-19}}}eV$

$\displaystyle \Rightarrow E=95.7MeV$

But experimentally, electrons emitted during β-decay are found to have only 2 to 3 MeV of energy.

So, existence of electrons in the composition of nucleus is not justified.

Reason 2 :- Nuclear magnetic moments

Let us compare magnetic dipole moments of electrons and protons.

For electron (Bohr magnetron),

$\displaystyle {{\mu }_{B}}=\frac{eh}{4\pi {{m}_{e}}}$ …..(i)

For proton (Nuclear magnetron),

$\displaystyle {{\mu }_{N}}=\frac{eh}{4\pi {{m}_{p}}}$ …..(ii)

Dividing (i) by (ii), we get

$\displaystyle \frac{{{\mu }_{B}}}{{{\mu }_{N}}}=\frac{{{m}_{p}}}{{{m}_{e}}}=\frac{1836{{m}_{e}}}{{{m}_{e}}}=1836$

⇒ μ_B = 1836μ_N

⇒ Magnetic moment of electrons is about 2000 times more than protons.

If electron exist in the nucleus, the nuclear magnetic moment should be of the order of magnetic moment of electron, but it’s not. So nuclei cannot contain electrons.

Reason 3 :- Nuclear spin

Electrons and protons both have spins of 1/2. Deuteron ₁H² (an isotope of hydrogen) is known to have a mass roughly equal to two protons. If the deuteron nucleus contains two protons and one electron (whose mass is small enough to not worry about here), then the possible chances of spins of electrons and protons are…

Sr. No.	proton	proton	electron	Total spin
(a)	↑ (+1/2)	↑ (+1/2)	↑ (+1/2)	+3/2
(b)	↑ (+1/2)	↑ (+1/2)	↓ (-1/2)	+1/2
(c)	↑ (+1/2)	↓ (-1/2)	↓ (-1/2)	-1/2
(d)	↓ (-1/2)	↓ (-1/2)	↓ (-1/2)	-3/2

So here the theoretical total spin comes out to be from -1/2 to +3/2.

But the experimental nuclear spin of deuterium is +1

Hence its nucleus cannot contain an electron.

Reason 4 :- Dual role of electrons in the atom

The presence of a few electrons in the nucleus and the rest as peripheral around the nucleus exhibit dual role of electrons in the atomic structure which is very difficult to visualize. So there is no role of electron in the composition of nucleus.

Reason 5 :- Finite size of electron

In the case of heavy atoms, the required number of electrons to render atom as a whole neutral, comes out to be very large. If the electron is assumed to be spherical of finite dimensions, the existence of large number of electrons in the nucleus will make the dimensions of the nucleus bigger than the experimentally measured values, a contradiction to the observed facts.

Proton-Neutron hypothesis

(Composition of Nucleus)

Proton-neutron hypothesis was put forward by Heisenberg for composition of nucleus after the discovery of neutron by Chadwick(in 1932).

According to this hypothesis, protons and neutrons are the main building blocks in the composition of nucleus.

According to proton-neutron hypothesis a nucleus of mass number A and atomic number Z contains, Z protons and (A-Z) neutrons. Since an atom is electrically neutral, therefore, number of peripheral electrons must be equal to Z, i.e., the number of protons inside the nucleus.

This hypothesis removed all the discrepancies of proton-electron hypothesis.

Neutron is a neutral particle having no electric charge. Proton is slightly lighter than a Neutron and both protons and neutrons are aggregately called “nucleons“.

mass of proton, m_p = 1.6726 × 10^-27 Kg = 1.007825 amu

mass of neutron, m_n = 1.6749 × 10^-27 Kg = 1.008665 amu

Atomic number of an element is the total number of protons present inside the nucleus. As atom is electrically neutral, so atomic number is also equal to the number of electrons revolving in orbits around the nucleus of the atom. It is represented by Z.

Mass number of an element is the total number of protons and neutrons present inside the nucleus of an atom. It is represented by A.

So for an element _ZX^A, the composition of nucleus/atom

number of protons = Z

number of electrons = Z

number of nucleons = A

number of neutrons = (A – Z)

Next Topic :- Discovery of Neutron

Previous Topic :- Electron Volt (eV)

Composition of Nucleus

Composition of Nucleus

Proton-Electron hypothesis (1930)

(Composition of Nucleus)

Failure of Proton-Electron hypothesis

(Composition of Nucleus)

Proton-Neutron hypothesis

(Composition of Nucleus)

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