Assertion : For a gaseous reaction : 2B `to` A , the equilibrium constant `K_p` is less than `K_c`.
Reason: `K_p` is related to `K_c` as `K_p=K_c(RT)^(Deltan_g)`

Options

A. Assertion and reason both are correct statements and Reason is correct explanation for assertion.
B. Assertion and reason both are correct statement but reason is not correct explanation for assertion
C. Assertion is correct statement but reason is wrong statement.
D. Assertion is wrong statement but reason is correct statement

Answer

To solve the question, we will analyze the assertion and the reason provided regarding the relationship between the equilibrium constants \( K_p \) and \( K_c \) for the reaction \( 2B \rightleftharpoons A \).

### Step-by-step Solution:

1. **Identify the Reaction and Variables**:
The given reaction is:
\[ 2B \rightleftharpoons A \]
Here, we have 2 moles of gas \( B \) on the reactant side and 1 mole of gas \( A \) on the product side.

2. **Calculate \( \Delta n_g \)**:
\( \Delta n_g \) is defined as the change in the number of moles of gas, calculated as:
\[ \Delta n_g = \text{(moles of gaseous products)} - \text{(moles of gaseous reactants)} \]
For our reaction:
- Moles of gaseous products = 1 (from \( A \))
- Moles of gaseous reactants = 2 (from \( 2B \))
Thus,
\[ \Delta n_g = 1 - 2 = -1 \]

3. **Relate \( K_p \) and \( K_c \)**:
The relationship between \( K_p \) and \( K_c \) is given by the formula:
\[ K_p = K_c (RT)^{\Delta n_g} \]
Substituting \( \Delta n_g = -1 \):
\[ K_p = K_c (RT)^{-1} = \frac{K_c}{RT} \]

4. **Analyze the Relationship**:
Since \( R \) (the gas constant) and \( T \) (temperature) are both positive values, \( RT \) is greater than 1. Therefore:
\[ K_p = \frac{K_c}{RT} \implies K_p < K_c \]
This confirms that \( K_p \) is indeed less than \( K_c \).

5. **Conclusion**:
- The assertion states that \( K_p \) is less than \( K_c \), which is true.
- The reason provided explains the relationship correctly, stating that \( K_p \) is related to \( K_c \) as \( K_p = K_c (RT)^{\Delta n_g} \).

Thus, both the assertion and the reason are correct, and the reason correctly explains the assertion.

### Final Answer:
- **Assertion**: True
- **Reason**: True
- **Explanation**: The reason correctly explains the assertion.