The average density of nuclear matter is and the mass of a nucleon is

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

The average density of nuclear matter is

2.3\times10^{17}\,\text{kg m}^{-3}

and the mass of a nucleon is

1.67\times10^{-27}\,\text{kg}

. Treat every nucleus as a uniform sphere of radius

R

containing

A

nucleons. (a) Derive an expression for

R

in terms of

A

. (b) Use this expression to calculate the radius of the iron nucleus

^{56}\mathrm{Fe}

. Give your answer in femtometres (1\,fm

=10^{-15}

\,m). (c) Estimate the average centre-to-centre separation between neighbouring nucleons in

^{56}\mathrm{Fe}

and comment on how this value supports the short-range character of the nuclear force.