CBSE Class 12 · 2023 · Modern PhysicsShort Answer

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(b)(i) How is the size of a nucleus found experimentally? Write the relation between the radius and the mass number of a nucleus. (ii) Prove that the density of a nucleus is independent of its mass number.

Answer: Scattering gives size; $R = R_{0} A^{1/3}$ ; $ρ = 3 m /4 π R_{0}^{3}$ .

Solution

(i) The nuclear size is found from scattering experiments (e.g.

α

-particle or fast-electron scattering): the distance of closest approach in Rutherford scattering gives an upper limit to the radius. The radius is related to the mass number by

R = R_{0} A^{1/3}, R_{0} \approx 1.2 fm .

(ii) Density:

ρ = \frac{A m}{\frac{4}{3} π ( R _{0} A ^{1/3} ) ^{3}} = \frac{3 m}{4 π R _{0}^{3}},

which contains no

A

, so the nuclear density is independent of the mass number.

R = R_{0} A^{1/3}; ρ = \frac{3 m}{4 π R _{0}^{3}}

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CBSE Class 12 · 2023 · Modern PhysicsShort Answer

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