Question

Prove that the density of nuclear matter is same for all nuclei.

Answer 1

Nuclear density is the ratio of the total mass of the nucleus to its total volume. We assume the nucleus to be a sphere.

Mass of nucleus (M) ≈ A . mp

Where,

A = Mass number

mp = Average mass of a nucleon

Radius of nucleus (R) = R₀A^1/3

Volume of nucleus (V) = `4/3 pi R^3`

Density (ρ) = `"Mass"/"Volume"`

= `(A * m_p)/(4/3 pi R^3)`

Substituting the expression for R:

ρ = `(A * m_p)/(4/3 pi(R_0 A^(1//3))^3)`

= `(A * m_p)/(4/3 pi R_0^3 A)`

Cancelling A from the numerator and denominator:

ρ = `(3 m_p)/(4 pi R_0^3)`

Since m_p, π, and R₀ are constants, the density ρ is constant for all nuclei and does not depend on the mass number A.