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

Answer

To solve the problem, we need to find the number of nucleons in germanium (Ge) given that its radius is twice that of beryllium (Be). The relationship between the radius of a nucleus and its number of nucleons is given by the formula:

\[ R \propto A^{1/3} \]

where \( R \) is the radius of the nucleus and \( A \) is the number of nucleons.

### Step-by-Step Solution:

1. **Identify the given information:**
- The radius of germanium (Ge) is twice the radius of beryllium (Be).
- The atomic mass number of beryllium (Be) is 9 (which means it has 9 nucleons).

2. **Set up the relationship using the radius formula:**
- Let \( R_{Be} \) be the radius of beryllium and \( R_{Ge} \) be the radius of germanium.
- According to the problem, \( R_{Ge} = 2R_{Be} \).

3. **Use the proportionality of radius and nucleons:**
- For beryllium, we have:
\[ R_{Be} \propto A_{Be}^{1/3} \]
where \( A_{Be} = 9 \).
- For germanium, we have:
\[ R_{Ge} \propto A_{Ge}^{1/3} \]
where \( A_{Ge} \) is the number of nucleons in germanium that we need to find.

4. **Set up the ratio of the radii:**
- From the relationship of the radii, we can write:
\[ \frac{R_{Ge}}{R_{Be}} = \frac{A_{Ge}^{1/3}}{A_{Be}^{1/3}} \]
- Substituting the known values:
\[ \frac{2R_{Be}}{R_{Be}} = \frac{A_{Ge}^{1/3}}{9^{1/3}} \]

5. **Simplify the equation:**
- This simplifies to:
\[ 2 = \frac{A_{Ge}^{1/3}}{9^{1/3}} \]

6. **Cross-multiply to solve for \( A_{Ge} \):**
- Rearranging gives:
\[ A_{Ge}^{1/3} = 2 \times 9^{1/3} \]
- Cubing both sides:
\[ A_{Ge} = (2 \times 9^{1/3})^3 \]

7. **Calculate \( A_{Ge} \):**
- We know \( 9^{1/3} = 3 \), so:
\[ A_{Ge} = (2 \times 3)^3 = 6^3 = 216 \]

8. **Final answer:**
- The number of nucleons in germanium (Ge) is **216**.