From the relation R = R₀ A¹/3}, where R₀ is ...

NCERT Class XII Chapter
Nuclei
Questions With Solutions

Question : 21 of 31

Marks: +1, -0

From the relation R =

R_0 A^{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).

Solution:

Density of nuclear matter =

\frac{\text{Mass of nucleus}}{\text{Volume}}

ρ =

\frac{A \times 1\,\mathrm{amu}}{\frac{4}{3}\pi R^3}

, where R =

R_0 A^{1/3}

Density, ρ =

\frac{A \times 1\,\mathrm{amu}}{\frac{4}{3}\pi R_0^3 A}

\frac{1\,\mathrm{amu}}{\frac{4}{3}\pi R_0^3}

\frac{3\,\mathrm{amu}}{4\pi R_0^3}

R_0

is constant, ρ is constant

So, nuclear density is constant irrespective of mass number or size.

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