JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Modern Physics

The ratio of mass densities of nuclei of

^{40} C a

and

^{16} O

is close to:

(A)0.1
(B)5
(C)2
(D)1✓ Correct

Answer: (D)

Solution

The physics to hold on to is that every nucleus has essentially the same density. The nuclear radius goes as

R \propto A^{1/3}

, so the volume goes as

R^{3} \propto A

, while the mass is also proportional to

A

. Density is mass over volume,

ρ \propto \frac{A}{A}

, a constant that does not depend on the mass number. So whether we take

^{40} Ca

^{16} O

the densities are the same, and their ratio is close to 1.

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option

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