An isotone of `""_(32)^(76)Ge` is

Options

A. `""_(32)^(77)Ge `
B. `""_(33)^(77)As`
C. `""_(34)^(77)Se`
D. `""_(36)^(81)Kr`

Explanation

To find an isotone of germanium-76 (represented as \( _{32}^{76}Ge \)), we need to follow these steps:

### Step 1: Identify the Mass Number and Atomic Number
The given isotope is \( _{32}^{76}Ge \). Here:
- The atomic number (Z) is 32, which represents the number of protons in germanium.
- The mass number (A) is 76, which is the total number of protons and neutrons.

### Step 2: Calculate the Number of Neutrons
To find the number of neutrons (N), we can use the formula:
\[ N = A - Z \]
Substituting the values:
\[ N = 76 - 32 = 44 \]
So, germanium-76 has 44 neutrons.

### Step 3: Define Isotones
Isotones are nuclides that have the same number of neutrons but different numbers of protons. Therefore, we need to find another nuclide that also has 44 neutrons.

### Step 4: Search for Isotones
We will check various elements to find one that has 44 neutrons:
1. **Arsenic (As)**:
- Atomic number = 33
- Mass number = \( N + Z = 44 + 33 = 77 \)
- Thus, \( _{33}^{77}As \) has 44 neutrons.

2. **Selenium (Se)**:
- Atomic number = 34
- Mass number = \( N + Z = 44 + 34 = 78 \)
- Thus, \( _{34}^{78}Se \) has 44 neutrons.

3. **Krypton (Kr)**:
- Atomic number = 36
- Mass number = \( N + Z = 44 + 36 = 80 \)
- Thus, \( _{36}^{80}Kr \) has 44 neutrons.

### Step 5: Conclusion
Among the options provided, the element that has the same number of neutrons (44) as germanium-76 is arsenic-77 (\( _{33}^{77}As \)). Therefore, the isotone of \( _{32}^{76}Ge \) is \( _{33}^{77}As \).

### Final Answer
The isotone of \( _{32}^{76}Ge \) is \( _{33}^{77}As \).

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