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

Options

A. `._(32)^(77)Ge`
B. `._(33)^(77)As`
C. `._(34)^(77)Se`
D. `._(34)^(78)Se`

Answer

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

### Step 1: Understand the concept of isotones
Isotones are atoms that have the same number of neutrons but different numbers of protons.

### Step 2: Calculate the number of neutrons in \( _{32}^{76}\text{Ge} \)
The number of neutrons (N) can be calculated using the formula:
\[ N = A - Z \]
where \( A \) is the mass number and \( Z \) is the atomic number (number of protons).

For germanium \( _{32}^{76}\text{Ge} \):
- Mass number \( A = 76 \)
- Atomic number \( Z = 32 \)

Calculating the number of neutrons:
\[ N = 76 - 32 = 44 \]

### Step 3: Find an element with 44 neutrons
Now we need to find another element that also has 44 neutrons. We can express this as:
\[ N = A - Z \implies Z = A - 44 \]

### Step 4: Check possible candidates
We can check various mass numbers \( A \) to find corresponding atomic numbers \( Z \) that yield 44 neutrons.

1. If \( A = 78 \):
\[ Z = 78 - 44 = 34 \quad \text{(Selenium, } _{34}^{78}\text{Se)} \]

2. If \( A = 77 \):
\[ Z = 77 - 44 = 33 \quad \text{(Arsenic, } _{33}^{77}\text{As)} \]

3. If \( A = 75 \):
\[ Z = 75 - 44 = 31 \quad \text{(Gallium, } _{31}^{75}\text{Ga)} \]

### Step 5: Identify isotones
From the calculations, we find:
- \( _{34}^{78}\text{Se} \) has 44 neutrons.
- \( _{33}^{77}\text{As} \) has 44 neutrons.
- \( _{31}^{75}\text{Ga} \) has 44 neutrons.

Thus, the isotones of \( _{32}^{76}\text{Ge} \) include \( _{34}^{78}\text{Se} \) and \( _{33}^{77}\text{As} \).

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

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