General Properties of Nucleus and Atomic Mass Unit

The central core of an atom which contains all the atoms positive charge and most of its mass is known as an atomic nucleus. The branch of physics dealing with the study of an atomic nucleus is called nuclear physics.

Discovery of Atomic Nucleus

Atomic nucleus was discovered by α-particle scattering experiment. In this experiment, α-particles from a radioactive source are passed through a thin gold foil of thickness 2.1 × 10^-7 m. The α-particles scattered in different directions are observed through a zinc sulphide screen and a microscope. They found that most of the α-particles passed straight through the gold foil, very few α-particles scattered through a large angle and rarely a α-particle rebounds. It was concluded that an atom has the highly dense central part where almost all of the mass and all of the atom’s positive charge is concentrated in a very small region as compared to that of the atom as a whole. The central part of the atom was called nucleus.

Constituents of Nucleus

All atomic nuclei except ₁H¹ are made of the protons and neutrons. A proton has a positive charge of the same magnitude as that of an electron, but a neutron is electrically neutral. These protons and neutrons of an atom are collectively called nucleons of that atom.

A species of nucleus known as nuclide is represented by _ZX^A where Z is the atomic number which indicates a number which indicates a number of protons, A is the mass number which indicates a total number of nucleons and X is the chemical symbol of the species. The number of neutrons is given by N = A – Z. For example, in ₇N¹⁴ the atomic number Z = 7, mass number A = 14, number of neutrons N = A – Z = 14 – 7 = 7 and N represents nitrogen.

General Properties of Nucleus

1. Size
   The nucleus is about 10,000 times smaller than the atom. The empirical formula for the nuclear radius is \(R = r_0A^{1/3} \) where A is the mass number and \(r_0 = 1.2 \times 10^{-15} m = 1.2 Fm \)
2. Charge
   The nuclei consist of protons and neutrons. Protons are positively charged and neutrons are neutral. So the nuclei are positively charged. The charge of a nuclide _ZX^A is Ze.
3. Mass
   Since the nucleus consists of protons and neutrons, the mass of the nucleus is the sum of masses of nucleons.
   $$ \text {Assumed mass} = Z\: m_p + N\: m_n $$
   where Z is the atomic number, N is neutron number m_p is a mass of a proton and m_n is a mass of a neutron.
4. Nuclear density
   The mass per unit volume of a nucleus is called nuclear density.
   \begin{align*} \text {Nuclear density,} \rho &= \frac {\text {Nuclear mass}}{\text {Nuclear volume}} \\ &= \frac {Am_N}{4/3 \pi R^3} \\ &= \frac {Am_N}{4/3 \pi (r_0A^{1/3})^3} \\ &= \frac {3m_NA}{4\pi r_0^3A} \\ \text {where} \: m_N \: \text { is mass of a nucleon. So,} \\ \rho &= \frac {3\times 1.66 \times 10^{-27}}{4\pi (1.2 \times 10^{-15})^3}kg/m^3 \\ &= 2.3 \times 10^{17} kgm{-3} \\ \end{align*}
   this shows that the density of nucleus is very high and is independent with A.
5. Nuclear spin and magnetic moment
   Protons and neutrons are in continuous motion in discrete quantized orbits. The nucleons have internal angular momentum called spin. As a result, they possess magnetic momentum associated with their orbital motion and spin.

Atomic Mass and Atomic Mass Unit

The abbreviated mass of atoms, nucleus and fundamental particles (electrons, protons, neutrons etc.) are called atomic mass unit. One amu is defined as 1/12 of the mass of one ₆C¹² atoms. As 12 g of ₆C¹² contains 6.023 × 10²³ atoms of ₆C¹², so mass of one ₆C¹² atom is

\begin{align*} \frac {12}{6.023 \times 10^{23}}g \\ 1 \:\text {amu} &= \frac {1}{12} \left (\frac {12}{6.023 \times 10^{23}} \right )g \\&= 1.66 \times 10^{-24} \\ \therefore 1\: amu &= 1.66 \times 10^{-24} \\ &= 1.66 \times 10^{-27} kg \\ \end{align*}

\begin{align*}\text {On atomic scale, mass of protons, neutrons and electrons are,} \\ m_p = 1.672622 \times 10^{-27} g = 1.007276 \: amu \\ m_n &= 1.674927 \times 10^{-27} kg = 1.008665\: amu \\ m_e &= 9.10938 \times 10^{-31} \: kg = 0.000548580 \: amu \\ \end{align*}

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel.Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.