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  • 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)

Q. 13.21  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).

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Mass of an element with mass number A will be about A u. The density of its nucleus, therefore, would be

\\d=\frac{m}{v}\\ d=\frac{A}{\frac{4\pi }{3}R^{3}}\\d=\frac{A}{\frac{4\pi }{3}(R_{0}A^{1/3})^{3}}\\d=\frac{3}{4\pi R{_{0}}^{3}}

As we can see the above density comes out to be independent of mass number A and R0 is constant, so  matter density is nearly constant

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