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Atoms and Nuclei question

2024 · 31 Jan · Shift 2 · Q87

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Atoms and Nuclei
2024 · 31 Jan · Shift 2 · Q87

Atoms and Nuclei question

2024 · 31 Jan · Shift 2 · Q87

JEE MainPhysicsAtoms and NucleiNumerical+4 / −1

A nucleus has mass number

A_1

and volume

V_1

. Another nucleus has mass number

A_2

and Volume

V_2

. If relation between mass number is

A_2=4 A_1

, then

\frac{V_2}{V_1}=\underline{\hspace{2cm}}

.

Numerical answer

View written solutionFree

Correct answer: 4

Use the nuclear radius relation

For a nucleus, radius is given by $R = R_0 A^{1/3}$ where $A$ is the mass number.
Write volume in terms of radius

Nuclear volume is $V = \frac{4}{3}\pi R^3$

Substituting $R = R_0 A^{1/3}$ : $V = \frac{4}{3}\pi (R_0 A^{1/3})^3$
Simplify

$V = \frac{4}{3}\pi R_0^3 A$

So, $V \propto A$
Take ratio of volumes

Since $A_2 = 4A_1$ , $\frac{V_2}{V_1} = \frac{A_2}{A_1} = \frac{4A_1}{A_1} = 4$
Final answer

$\boxed{4}$

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