Given below are two statements : One is labelled as Assertion A and the other is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The nuclear density of nucides `"^(10)B_5,"^6Li_3,"^(56)Fe_(26),"^(20)Ne_(10)` and `"^(200)Bi_(83)` can be arranged as `rho_(Bi)^N gt rho_(Fe)^n gt rho_(Ne)^N gt rho_B^N gt rho_(Li)^N`.
Reasion : The radius `R` of nucleus is related to its mass number `A` as `R=R_(A)A^(I`,where `R_(0)` is a constant.
In the light of the above statements, choose the correct answer from the options given below :

Options

A. Both A and R are true and R is the correct explanation of A
B. A is false but R is true
C. Both A and R are true but R is NOT the correct explanation of A
D. A is true but R is false

Answer

To solve the given problem, we need to analyze both the Assertion (A) and the Reason (R) provided.

### Step 1: Analyze the Assertion (A)
The assertion states that the nuclear density of the nuclides \(^{10}B_5\), \(^{6}Li_3\), \(^{56}Fe_{26}\), \(^{20}Ne_{10}\), and \(^{200}Bi_{83}\) can be arranged as:
\[ \rho_{Bi}^N > \rho_{Fe}^N > \rho_{Ne}^N > \rho_{B}^N > \rho_{Li}^N \]
To evaluate this, we need to understand that the nuclear density (\(\rho\)) of a nucleus is given by the formula:
\[ \rho = \frac{mass}{volume} \]
The volume of a nucleus can be approximated using the formula:
\[ V \propto R^3 \propto A \]
where \(R\) is the radius of the nucleus and \(A\) is the mass number. The density can be expressed as:
\[ \rho \propto \frac{A}{R^3} \propto \frac{A}{A} = constant \]
This implies that nuclear density is approximately constant for different nuclei, leading us to conclude that the assertion is incorrect.

### Step 2: Analyze the Reason (R)
The reason states that the radius \(R\) of a nucleus is related to its mass number \(A\) as:
\[ R = R_0 A^{1/3} \]
This relationship is indeed correct. The radius of a nucleus increases with the cube root of its mass number, which is a well-established principle in nuclear physics.

### Step 3: Conclusion
From the analysis:
- The Assertion (A) is **false**.
- The Reason (R) is **true**.

Thus, the correct answer is that the Assertion is false while the Reason is true.

### Final Answer
The correct option is that Assertion A is false and Reason R is true.

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