Consider two nuclei one of `""^(70)Ge` and other of `""^(198)Au` and choose the correct statement (s) from the following

Options

A. The nuclei radius of `""^(70) Ge and ""^(198)Au` are same
B. The nuclei volume of `""^(70)Ge and ""^(198) Au` are same
C. The nuclear densities of both `""^(70)Ge and ""^(198)Au` are same
D. The force of attraction between nucleons is electrostatic froce only

Answer

To solve the problem regarding the nuclei of \(^{70}\text{Ge}\) (Germanium) and \(^{198}\text{Au}\) (Gold), we need to analyze the given statements about nuclear properties. Let's go through each statement step by step.

### Step-by-Step Solution

1. **Nuclear Radius Comparison**:
The formula for the nuclear radius \(R\) is given by:
\[ R = R_0 A^{1/3} \]
where \(R_0\) is a constant (approximately \(1.2 \times 10^{-15}\) m) and \(A\) is the atomic mass number. For \(^{70}\text{Ge}\), \(A = 70\) and for \(^{198}\text{Au}\), \(A = 198\). Since the atomic mass numbers are different, the radii will also be different. Therefore, the statement about nuclear radius being the same is **incorrect**.

2. **Nuclear Volume Comparison**:
The volume \(V\) of a nucleus can be approximated as:
\[ V = \frac{4}{3} \pi R^3 \]
Substituting the expression for \(R\):
\[ V = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A \]
Since the atomic mass numbers \(A\) are different for the two nuclei, the volumes will also be different. Thus, the statement about nuclear volume being the same is **incorrect**.

3. **Nuclear Density Comparison**:
The density \(\rho\) of a nucleus is given by:
\[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{A \cdot m_u}{\frac{4}{3} \pi R_0^3 A} = \frac{3 m_u}{4 \pi R_0^3} \]
Here, \(m_u\) is the atomic mass unit. Notice that the atomic mass \(A\) cancels out, indicating that the density of the nucleus is independent of the atomic mass number. Therefore, the density is the same for both nuclei. This statement is **correct**.

4. **Nature of Force of Attraction**:
The force of attraction between nucleons in a nucleus is not solely electrostatic; it also includes the strong nuclear force, which is the primary force holding the nucleus together. Therefore, the statement that the force of attraction between nuclei is electrostatic only is **incorrect**.

### Summary of Statements:
- **Nuclear radius is the same**: **Incorrect**
- **Nuclear volume is the same**: **Incorrect**
- **Nuclear density is the same**: **Correct**
- **Force of attraction is electrostatic only**: **Incorrect**

### Final Answer:
The only correct statement is that the **nuclear density is the same** for both \(^{70}\text{Ge}\) and \(^{198}\text{Au}\).