Atoms & Nuclei

JEE Main level, single correct, medium

11 of 239

Question 11 of 239

Read the following statements:
(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.
Choose the correct option from the following options.

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Answer: (B) (A) and (E) only.

Radius of nucleus is R=R0A13R={R}_{0}{A}^{\dfrac{1}{3}}, where, R0=1.2×10−15m{R}_{0}=1.2\times {10}^{-15}m and AA is mass number of nucleus.
Thus, R∝A13R\propto {A}^{\dfrac{1}{3}}
Volume of nucleus is V=43πR3⇒V∝R3⇒V∝AV=\dfrac{4}{3}\pi {R}^{3}\Rightarrow V\propto {R}^{3}\Rightarrow V\propto A.
Now, the density of nucleus is given by ρ=MV=mA43πR03A=m43πR03\rho =\dfrac{M}{V}=\dfrac{mA}{\dfrac{4}{3}\pi {R}_{0}^{3}A}=\dfrac{m}{\dfrac{4}{3}\pi {R}_{0}^{3}}
Thus, density is independent of AA.
Hence, only (A)\left(A\right) and (E)\left(E\right) are correct.

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