Question

Two nuclei have mass numbers A and B respectively. The density ratio of the nuclei is______.
Fill in the blank with the correct answer from the options given below.

• A. A : B
• B. √A : √B
• C. A² : B²
• D. 1 : 1

Answer 1

The Correct Option is D

Let's analyze the density of nuclei.

1. Density of Nucleus:

The density of a nucleus is approximately constant, regardless of its mass number.

2. Explanation:

The nucleus is composed of nucleons (protons and neutrons). The radius of a nucleus is given by:

R = R₀A^1/3

Where:

• R is the radius of the nucleus
• R₀ is a constant (approximately 1.2 fm)
• A is the mass number

The volume (V) of the nucleus is:

V = (4/3)πR³

V = (4/3)π(R₀A^1/3)³

V = (4/3)πR₀³A

The mass (M) of the nucleus is approximately proportional to the mass number A:

M ∝ A

The density (ρ) of the nucleus is:

ρ = M/V

ρ ∝ A / [(4/3)πR₀³A]

ρ ∝ 1 / [(4/3)πR₀³]

Since R₀ is a constant, the density ρ is also a constant, independent of the mass number A.

Therefore, the density ratio of two nuclei with mass numbers A and B is 1:1.

The correct answer is:

Option 4: 1 : 1