1 mole of a diatomic element `X_2` contains 34 and 40 moles of electrons and neutrons respectively. The isotopic formula of the element is:

Options

A. `""_(34)^(74)X`
B. `""_(17)^(37)X`
C. `""_(34)^(40)X`
D. `""_(20)^(40)X`

Answer

To solve the problem, we need to determine the isotopic formula of the diatomic element \( X_2 \) based on the given information about the number of electrons and neutrons.

### Step-by-Step Solution:

1. **Identify the Number of Electrons in \( X_2 \)**:
- We are told that 1 mole of the diatomic element \( X_2 \) contains 34 moles of electrons.
- Since \( X_2 \) has 2 atoms of \( X \), the number of electrons in one molecule of \( X_2 \) is 34.
- Therefore, the number of electrons in one atom of \( X \) is:
\[ \text{Electrons in } X = \frac{34}{2} = 17 \]

2. **Identify the Number of Neutrons in \( X_2 \)**:
- We are also told that 1 mole of \( X_2 \) contains 40 moles of neutrons.
- Thus, the number of neutrons in one molecule of \( X_2 \) is 40.
- Therefore, the number of neutrons in one atom of \( X \) is:
\[ \text{Neutrons in } X = \frac{40}{2} = 20 \]

3. **Determine the Number of Protons**:
- For a neutral atom, the number of protons is equal to the number of electrons.
- Since we found that there are 17 electrons in \( X \), the number of protons in \( X \) is also:
\[ \text{Protons in } X = 17 \]

4. **Calculate the Mass Number**:
- The mass number (A) of an element is the sum of the number of protons and neutrons.
- Therefore, the mass number of \( X \) is:
\[ A = \text{Protons} + \text{Neutrons} = 17 + 20 = 37 \]

5. **Write the Isotopic Formula**:
- The isotopic formula of an element is represented as \( \text{Element Symbol} \, A \) where \( A \) is the mass number and the atomic number (Z) is the number of protons.
- In this case, the element symbol for the atomic number 17 is Cl (Chlorine).
- Thus, the isotopic formula of the element \( X \) is:
\[ \text{Cl}^{37} \]

### Final Answer:
The isotopic formula of the element \( X \) is \( \text{Cl}^{37} \).

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