Why Nuclear Density is Nearly Constant

❓ Question

Given below are two statements:

• Assertion (A): The density of the copper ($^{64}\text{Cu}_{29}$) nucleus is greater than that of the carbon ($^{12}\text{C}_6$) nucleus.

• Reason (R): The nucleus of mass number $A$ has a radius proportional to $A^{1/3}$.

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🖼️ Question Image

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✍️ Short Explanation

This problem is based on:

👉 Nuclear radius
👉 Nuclear density
👉 Assertion-Reason concept.

Main idea:

Nuclear radius:

$$\boxed{ R=R_0A^{1/3} }$$

Hence nuclear volume:

$$V\propto R^3\propto A$$

and nuclear mass also:

$$M\propto A$$

Therefore nuclear density becomes approximately constant for all nuclei.

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🔷 Step 1 — Use Nuclear Radius Formula 💯

For nucleus:

$$\boxed{ R=R_0A^{1/3} }$$

Thus:

$$V\propto R^3$$
$$\Rightarrow V\propto A$$

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🔷 Step 2 — Mass of Nucleus

Mass of nucleus is approximately proportional to mass number:

$$M\propto A$$

Density:

$$\rho=\frac{M}{V}$$

Substitute proportionalities:

$$\rho\propto\frac{A}{A}$$
$$\boxed{ \rho=\text{constant} }$$

Thus all nuclei have nearly same density.

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🔷 Step 3 — Check Assertion and Reason

Assertion (A)

Says copper nucleus density is greater than carbon nucleus density.

❌ Incorrect

Because nuclear density is approximately same for all nuclei.

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Reason (R)

$$R\propto A^{1/3}$$

✔ Correct

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🔷 Step 4 — Final Conclusion

✔ Assertion (A) → Incorrect

✔ Reason (R) → Correct

Therefore:

$$\boxed{ \text{(A) is not correct but (R) is correct} }$$

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🔷 Step 5 — JEE Trap Alert 🚨

❌ Bigger nucleus means bigger density assume kar lena

❌ Radius relation yaad ho but density logic miss kar dena

Remember:

$$\boxed{ \text{Nuclear density is nearly constant} }$$

for almost all nuclei.

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✅ Final Answer

$$\boxed{ \text{(A) is not correct but (R) is correct} }$$

(Option 3)

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