Read the following statements: (A) Volume of the nucleus is directly proportional to the mass number. (B)…

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.

  1. (A) and (D) only.
  2. (A) and (E) only.
  3. (B) and (E) only.
  4. (A) and (C) only

Solution

Radius of nucleus is R=R0A13, where, R0=1.2×10-15 m and A is mass number of nucleus.

Thus, R∝A13

Volume of nucleus is V=43πR3⇒V∝R3⇒V∝A.

Now, the density of nucleus is given by ρ=MV=mA43πR03A=m43πR03

Thus, density is independent of A.

Hence, only A and E are correct.

Asked in: JEE Main 2022 (29 Jul Shift 2)

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