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 the isotope \( _{32}^{76}\text{Ge} \) (Germanium-76), we need to follow these steps:

### Step 1: Determine the number of neutrons in Germanium-76
The number of neutrons can be calculated using the formula:
\[ \text{Number of Neutrons} = \text{Mass Number} - \text{Atomic Number} \]
For Germanium-76:
- Mass Number = 76
- Atomic Number (number of protons) = 32

So, the number of neutrons in Germanium-76 is:
\[ \text{Number of Neutrons} = 76 - 32 = 44 \]

### Step 2: Identify the characteristics of isotones
Isotones are defined as atoms that have the same number of neutrons but different numbers of protons. Therefore, we need to find another element that has 44 neutrons.

### Step 3: Find an element with 44 neutrons
To find an isotone, we can use the formula again:
\[ \text{Mass Number} = \text{Number of Neutrons} + \text{Number of Protons} \]
Since we need the number of neutrons to be 44, we can express the mass number of the isotone as:
\[ \text{Mass Number} = 44 + Z \]
where \( Z \) is the atomic number (number of protons).

### Step 4: Check possible values for \( Z \)
We can check various atomic numbers \( Z \) to find a suitable isotone:
- If \( Z = 33 \) (Arsenic), then:
\[ \text{Mass Number} = 44 + 33 = 77 \quad \Rightarrow \quad _{33}^{77}\text{As} \]
- If \( Z = 31 \) (Gallium), then:
\[ \text{Mass Number} = 44 + 31 = 75 \quad \Rightarrow \quad _{31}^{75}\text{Ga} \]
- If \( Z = 34 \) (Selenium), then:
\[ \text{Mass Number} = 44 + 34 = 78 \quad \Rightarrow \quad _{34}^{78}\text{Se} \]

### Step 5: Conclusion
From the calculations, we find that:
- \( _{33}^{77}\text{As} \) (Arsenic-77) and \( _{34}^{78}\text{Se} \) (Selenium-78) are isotones of \( _{32}^{76}\text{Ge} \) since they both have 44 neutrons.

### Final Answer
An isotone of \( _{32}^{76}\text{Ge} \) is \( _{33}^{77}\text{As} \) or \( _{34}^{78}\text{Se} \).

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