The equation `alpha=(D-d)/((n-1)d)` is correctly matched for :

Options

A. `A hArr nB//2+nC//3`
B. `A hArr nB//3+(2n//3)C`
C. `A to(n//2)B+(n//4)C`
D. `A hArr (n//2)B+C`

Explanation

To solve the problem, we need to analyze the equation given and determine which reaction corresponds to it based on the degree of dissociation and the number of gaseous products formed.

### Step-by-Step Solution:

1. **Understand the Equation**:
The equation given is:
\[ \alpha = \frac{D - d}{(n - 1)d} \]
Here, \( \alpha \) is the degree of dissociation, \( D \) is the total number of moles after dissociation, \( d \) is the number of moles before dissociation, and \( n \) is the number of gaseous products formed from one mole of reactant.

2. **Identify the Variables**:
- \( \alpha \): Degree of dissociation
- \( D \): Total moles after dissociation
- \( d \): Initial moles before dissociation
- \( n \): Number of gaseous products formed from one mole of reactant

3. **Evaluate Each Option**:
We will check each option to see if the total number of gaseous products formed equals \( n \).

- **Option 1**: \( A \rightarrow \frac{nB}{2} + \frac{nC}{3} \)
- Total gaseous products = \( \frac{n}{2} + \frac{n}{3} \)
- Finding a common denominator (6):
\[ \frac{3n}{6} + \frac{2n}{6} = \frac{5n}{6} \neq n \]
- This option does not match.

- **Option 2**: \( A \rightarrow \frac{nB}{3} + \frac{2nC}{3} \)
- Total gaseous products = \( \frac{n}{3} + \frac{2n}{3} = n \)
- This option matches.

- **Option 3**: \( A \rightarrow \frac{nB}{2} + \frac{nC}{4} \)
- Total gaseous products = \( \frac{n}{2} + \frac{n}{4} \)
- Finding a common denominator (4):
\[ \frac{2n}{4} + \frac{n}{4} = \frac{3n}{4} \neq n \]
- This option does not match.

- **Option 4**: \( A \rightarrow \frac{nB}{2} + 1C \)
- Total gaseous products = \( \frac{n}{2} + 1 \)
- This does not equal \( n \) unless \( n = 2 \), which is not guaranteed.
- This option does not match.

4. **Conclusion**:
The only option that correctly matches the equation is **Option 2**.

### Final Answer:
**Option 2 is the correct match for the equation.**

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