From the relation R = $R_{0} A^{\frac{1}{3}}$ , where $R_{0}$ is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

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Solution

Density of nuclear matter $=$ Mass of nucleus/Volume of nucleus
$= \frac{A}{\frac{4}{3} π R^{3}}$
$= \frac{A}{\frac{4}{3} π (R_{0} A^{1 / 3})^{3}} = \frac{1}{\frac{4}{3} π R_{0}^{3}} = c o n s t a n t$

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From the relation R = R0A13 , where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Density of nuclear matter = Mass of nucleus/Volume of nucleus =A43πR3 =A43π(R0A1/3)3=143πR30=constant

From the relation R = $R_{0} A^{\frac{1}{3}}$ , where $R_{0}$ is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Density of nuclear matter $=$ Mass of nucleus/Volume of nucleus
$= \frac{A}{\frac{4}{3} π R^{3}}$
$= \frac{A}{\frac{4}{3} π (R_{0} A^{1 / 3})^{3}} = \frac{1}{\frac{4}{3} π R_{0}^{3}} = c o n s t a n t$