Read the following statements: Choose the correct option from the following options
A) Volume of the nucleus is directly proportional to the mass number
B) Volume of the nucleus is independent of mass number
C) Density of the nucleus is directly proportional to the mass number
D) Density of the nucleus is directly proportional to the cube root of the mass number
E) Density of the nucleus is independent of the mass number

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(A) and (D) only

(A) and (E) only

(B) and (E) only

(A) and (C) only

answer is B.

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Detailed Solution

The radius of nucleus is given by $R = R_{0} A^{1 / 3}$
Volume, $V = \frac{4}{3} π R^{3} = \frac{4}{3} π R_{0}^{3} A$
Mass $= m \times A$
Density, $(ρ) = \frac{M a s s}{V o l u m e} = \frac{m \times A}{\frac{4}{3} π R_{0}^{3} A} = \frac{m}{\frac{4}{3} π R_{0}^{3}}, ρ \propto A^{0}$
Here m= no. of protons or neutrons.
So density is independent of A.