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प्रश्न
From the relation R = R0A1/3, 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).
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उत्तर
We have the expression for nuclear radius as:
R = R0A1/3
Where,
R0 = Constant.
A = Mass number of the nucleus
Nuclear matter density, `rho = "Mass of the nucleus"/"Volume of the nucleus"`
Let m be the average mass of the nucleus.
Hence, mass of the nucleus = mA
`therefore rho = "mA"/(4/3 pi"R"^3) = "3mA"/(4pi ("R"_0 "A"^(1/3))^3) = (3"mA")/(4pi"R"_0^3 "A") = "3m"/(4pi"R"_0^3)`
Hence, the nuclear matter density is independent of A. It is nearly constant.
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