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 two nuclei, \(^{70}\text{Ge}\) (Germanium) and \(^{198}\text{Au}\) (Gold), we will analyze each option step by step.

### Step 1: Understanding the Nucleus Radius
The radius of a nucleus can be calculated using the formula:
\[ R = R_0 A^{1/3} \]
where \(R_0\) is a constant (approximately \(1.2 \times 10^{-15}\) m) and \(A\) is the mass number (atomic mass).

**For \(^{70}\text{Ge}\)**:
- \(A = 70\)
- \(R_{Ge} = R_0 (70)^{1/3}\)

**For \(^{198}\text{Au}\)**:
- \(A = 198\)
- \(R_{Au} = R_0 (198)^{1/3}\)

Since the atomic masses are different, the radii will also be different. Thus, the first option is **incorrect**.

### Step 2: Understanding the Nucleus Volume
The volume \(V\) of a nucleus can be calculated assuming it is spherical:
\[ V = \frac{4}{3} \pi R^3 \]
Substituting the radius formula into the volume formula gives:
\[ V = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A \]
This shows that the volume is directly proportional to the mass number \(A\).

Since \(A\) is different for the two nuclei, their volumes cannot be the same. Thus, the second option is **incorrect**.

### Step 3: Understanding Nuclear Density
The density \(\rho\) of a nucleus is given by:
\[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{A}{V} \]
Substituting the volume from the previous step:
\[ \rho = \frac{A}{\frac{4}{3} \pi R_0^3 A} = \frac{3}{4 \pi R_0^3} \]
Here, we see that the mass number \(A\) cancels out, indicating that the density is independent of the mass number and is a constant for all nuclei.

Thus, the nuclear density of both \(^{70}\text{Ge}\) and \(^{198}\text{Au}\) is the same. Therefore, the third option is **correct**.

### Step 4: Understanding the Force of Attraction Between Nuclei
The force of attraction between nucleons (protons and neutrons) in a nucleus is primarily due to the strong nuclear force, not just the electrostatic force. The electrostatic force acts between charged particles, but the strong nuclear force is what holds the nucleus together.

Thus, the fourth option is **incorrect**.

### Conclusion
After analyzing all the options, the only correct statement is:
- The nuclear density of both \(^{70}\text{Ge}\) and \(^{198}\text{Au}\) are the same.

### Final Answer
The correct option is **C**.