The radius of germanium `(Ge)` nuclide is measured to be twice the radius of `._(4)^(9)Be`. The number of nucleons in `Ge` are

Options

A. `73`
B. `74`
C. `75`
D. `72`

Answer

To solve the problem, we need to find the number of nucleons in the germanium (Ge) nuclide given that its radius is twice that of the beryllium (Be) nuclide.

### Step-by-Step Solution:

1. **Understand the relationship between radius and mass number:**
The radius of a nucleus is related to its mass number (A) by the formula:
\[ R \propto A^{1/3} \]
This implies that the radius \( R \) is proportional to the cube root of the mass number \( A \).

2. **Set up the ratio of the radii:**
Let \( R_{Be} \) be the radius of beryllium and \( R_{Ge} \) be the radius of germanium. According to the problem:
\[ R_{Ge} = 2 R_{Be} \]

3. **Express the radii in terms of mass numbers:**
Using the proportionality, we can write:
\[ R_{Be} \propto A_{Be}^{1/3} \quad \text{and} \quad R_{Ge} \propto A_{Ge}^{1/3} \]
Therefore, we can express the ratio of the radii as:
\[ \frac{R_{Ge}}{R_{Be}} = \left(\frac{A_{Ge}}{A_{Be}}\right)^{1/3} \]

4. **Substituting the known values:**
We know that the atomic mass (mass number) of beryllium \( A_{Be} = 9 \). Substituting this into the ratio gives:
\[ 2 = \left(\frac{A_{Ge}}{9}\right)^{1/3} \]

5. **Cubing both sides to eliminate the cube root:**
\[ 2^3 = \frac{A_{Ge}}{9} \]
\[ 8 = \frac{A_{Ge}}{9} \]

6. **Solving for \( A_{Ge} \):**
Multiply both sides by 9:
\[ A_{Ge} = 8 \times 9 = 72 \]

7. **Conclusion:**
The number of nucleons in germanium (Ge) is equal to its atomic mass, which we have found to be:
\[ \text{Number of nucleons in Ge} = 72 \]

### Final Answer:
The number of nucleons in germanium (Ge) is **72**.