Composition of Nucleus:

An atom has a positively charged nucleus. The radius of the nucleus is smaller than the radius of an atom by a factor of 10⁴.

More than 99% mass of the atom is concentrated in the nucleus.

According to the proton-neutron hypothesis by Heisenberg’s in 1932 protons and neutrons are the main building blocks of the nuclei of all the atoms.

Thus nucleus of mass number A

And atomic number Z, contains Z protons

And A – Z = neutrons

The proton gives the positive charge to the nucleus while protons and neutrons together gives its mass.

To neutralize the positive charge of the nucleus is to make the atom electrically neutral, the number of extra nuclear electron is Z

Atomic Mass Unit: 1 amu = 1/12 x mass of carbon-12 atom.

= (1/12) x 1.9926 x 10^-26 kg

1 amu = 1.660565 x 10^-27 kg

1 amu = 931 MeV

Mass of an electron, m_e = 0.00055 amu

Mass of an P⁺, m_p = 1.0073 amu

Mass of neutron, m_n = 1.0086 amu

Mass of a hydrogen atom = m_p + m_n

= 1.0073 amu

Nuclear mass density:- As the volume of the nucleus is directly proportional to its mass number A, so the density of the nucleus is in depend of the size of the nucleus.

Let A be the mass number and R be the radius of the nucleus. If m is the average mass of the nucleon then mass of nucleus = m A    — (1)

Volume of nucleus = (4/3) π R³  — (2)

From statement,

(4/3) π R³ ∝ A

-->  R³ ∝ A

-->  R ∝ A^1/3

-->  R = R_o A^1/3              — (3)

Where R_o = empirical constant = propos here constant

= 1.2 x 10^-15 m

From equation (2) & (3)

Volume of nucleus, V = (4/3) π (R_o A^1/3)³

V = (4/3 ) π R_o³ A

Nuclear density = Mass of nucleus/Volume if nucleus

= m A/(4/3) π R_o³ A

= 3 m/(4 π R_o³)

ρ = 3m/(4 π R_o³)

Clearly nucleus density is independent of mass number A or the size of the nucleus substituting all the values,

m = 1.67 x 10^-27 kg

ρ = 3 x (1.67 x 10^-27)/(4 x 3.14) x (1.2 x 10^-15)³

ρ = 2.30 x 10¹⁷ kg/m³