Question 136: Atoms & Nuclei

Question

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

Accepted Answer

The radius $ R $ of a nucleus is given by the empirical relation:
$$ R = r_0 A^{\frac{1}{3}}, $$
where $ r_0 $ is a constant and $ A $ is the mass number.
The volume $ V $ of the nucleus is approximately that of a sphere:
$$ V = \frac{4}{3}\pi R^3. $$
Substituting the expression for $ R $ into the volume formula:
$$ V = \frac{4}{3}\pi \left(r_0 A^{\frac{1}{3}}ight)^3 = \frac{4}{3}\pi r_0^3 A. $$
The mass density $ ho $ is defined as the mass (which is proportional to $ A $) divided by the volume:
$$ ho = \frac{A}{V} = \frac{A}{\frac{4}{3}\pi r_0^3 A} = \frac{1}{\frac{4}{3}\pi r_0^3}. $$
Notice that $ A $ cancels out in the numerator and denominator, so the density is:
$$ ho = 	ext{constant}, $$
meaning it is independent of the mass number $ A $.
Thus, the correct option is:
Option B: Independent of A.

Answer

$A^{\frac{2}{3}}$

Answer

Independent of A

Answer

$A^3$

Answer

$A^{\frac{1}{3}}$

Atoms & Nuclei

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

Choose the correct answer: