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

Options

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

Explanation

To find the number of nucleons in germanium (Ge) given that its nucleus radius is twice that of beryllium (Be), we can follow these steps:

### Step 1: Understand the relationship between nucleus radius and mass number
The radius \( R \) of a nucleus is given by the formula:
\[ R = R_0 A^{1/3} \]
where \( R_0 \) is a constant and \( A \) is the mass number (number of nucleons).

### Step 2: Set up the equation for the radii of germanium and beryllium
Let \( A_{Ge} \) be the mass number of germanium and \( A_{Be} \) be the mass number of beryllium. According to the problem, the radius of germanium is twice that of beryllium:
\[ R_{Ge} = 2 R_{Be} \]

### Step 3: Substitute the radius formula into the equation
Using the formula for the radius, we can express this as:
\[ R_0 A_{Ge}^{1/3} = 2 R_0 A_{Be}^{1/3} \]
Here, \( R_0 \) cancels out from both sides:
\[ A_{Ge}^{1/3} = 2 A_{Be}^{1/3} \]

### Step 4: Cube both sides to eliminate the exponent
Cubing both sides gives:
\[ A_{Ge} = 2^3 A_{Be} \]
This simplifies to:
\[ A_{Ge} = 8 A_{Be} \]

### Step 5: Substitute the known mass number of beryllium
The mass number of beryllium \( A_{Be} \) is given as 9:
\[ A_{Ge} = 8 \times 9 \]

### Step 6: Calculate the mass number of germanium
Calculating this gives:
\[ A_{Ge} = 72 \]

### Conclusion
The number of nucleons in germanium is 72.