From the equation $R = R_{o} A^{\frac{1}{3}}$ , show that the nuclear matter density is nearly constant. [Where $R_{o}$ is a constant and A is the mass number.]

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Solution

Total mass of nucleus $\approx m_{p} A$
Hence the nuclear mass density= $\frac{M}{V}$
$= \frac{m_{p} A}{\frac{4}{3} π R^{3}}$
$= \frac{m_{p} A}{\frac{4}{3} π (R_{0}^{3} A)}$
$= \frac{3 m_{p}}{4 π R_{0}^{3}}$
which is a constant.

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From the equation R=RoA13, show that the nuclear matter density is nearly constant. [Where Ro is a constant and A is the mass number.]

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From the equation $R = R_{o} A^{\frac{1}{3}}$ , show that the nuclear matter density is nearly constant. [Where $R_{o}$ is a constant and A is the mass number.]

Total mass of nucleus $\approx m_{p} A$
Hence the nuclear mass density= $\frac{M}{V}$
$= \frac{m_{p} A}{\frac{4}{3} π R^{3}}$
$= \frac{m_{p} A}{\frac{4}{3} π (R_{0}^{3} A)}$
$= \frac{3 m_{p}}{4 π R_{0}^{3}}$
which is a constant.