## General Properties of Nucleus and Atomic Mass Unit

Subject: Physics

#### Overview

The central core of an atom which contains all the atoms positive charge and most of its mass is known as an atomic nucleus. This note provides us an information on general properties of a nucleus and atomic mass unit.
##### 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 ZXA 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 ZXA 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 mp is a mass of a proton and mn 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.

##### Things to remember

The central core of an atom which contains all the atoms positive charge and most of its mass is known as an atomic nucleus.

These protons and neutrons of an atom are collectively called nucleons of that atom.

Protons and neutrons are in continuous motion in discrete quantized orbits. The nucleons have internal angular momentum called spin.

The mass per unit volume of a nucleus is called nuclear density.

The abbreviated mass of atoms, nucleus and fundamental particles (electrons, protons, neutrons etc.) are called atomic mass unit.

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