An element with mass number 81 contains 31.7% more neutrons as compared to protons. Find the symbol of the element.

Options

A. `""_(34)^(81)Se`
B. `""_(35)^(81)Br`
C. `""_(36)^(81)Kr`
D. `""_(37)^(81)Rb`

Explanation

To solve the problem, we need to find the symbol of the element with a mass number of 81, given that it has 31.7% more neutrons than protons. Let's break this down step by step.

### Step-by-Step Solution:

1. **Define Variables**:
Let the number of protons be represented by \( X \).

2. **Calculate Neutrons**:
According to the problem, the number of neutrons is 31.7% more than the number of protons. This can be expressed mathematically as:
\[ \text{Number of Neutrons} = X + 0.317X = 1.317X \]

3. **Use the Mass Number**:
The mass number (A) of an element is the sum of the number of protons and neutrons. Given that the mass number is 81, we can write:
\[ A = \text{Number of Protons} + \text{Number of Neutrons} \]
Substituting the values we have:
\[ 81 = X + 1.317X \]
Simplifying this gives:
\[ 81 = 2.317X \]

4. **Solve for Protons**:
To find \( X \), we rearrange the equation:
\[ X = \frac{81}{2.317} \]
Calculating this gives:
\[ X \approx 35 \]
Therefore, the number of protons is 35.

5. **Calculate Neutrons**:
Now, we can find the number of neutrons:
\[ \text{Number of Neutrons} = 1.317 \times 35 \approx 46 \]

6. **Determine the Element**:
The element with 35 protons is Bromine (Br). The mass number is the sum of protons and neutrons, which we calculated as:
\[ \text{Mass Number} = 35 + 46 = 81 \]
Thus, the symbol of the element is:
\[ \text{Br}^{81} \]

### Final Answer:
The symbol of the element is \( \text{Br}^{81} \).