For a rigid diatomic molecule, univerisal gas constant `R = mc_(p)`, where `'C_(p)'` is the molar specific heat at constant pressure and 'n' is a number. Hence n is equal to

Options

A. 0.2257
B. 0.4
C. 0.2857
D. 0.3557

Answer

To solve the problem, we need to find the value of \( n \) in the equation \( R = mc_p \) for a rigid diatomic molecule, where \( R \) is the universal gas constant and \( c_p \) is the molar specific heat at constant pressure.

### Step-by-Step Solution:

1. **Understand the given equation**:
The equation provided is \( R = mc_p \). Here, \( R \) is the universal gas constant, \( m \) is a number we need to find, and \( c_p \) is the molar specific heat at constant pressure.

2. **Identify the specific heat for a diatomic gas**:
For a diatomic gas, the molar specific heat at constant pressure \( c_p \) is given by:
\[ c_p = \frac{7}{2} R \]
This is a known value for diatomic gases.

3. **Substitute \( c_p \) into the equation**:
Now we can substitute the expression for \( c_p \) into the original equation:
\[ R = m \left(\frac{7}{2} R\right) \]

4. **Simplify the equation**:
To isolate \( m \), we can rearrange the equation:
\[ R = \frac{7}{2} m R \]
We can divide both sides by \( R \) (assuming \( R \neq 0 \)):
\[ 1 = \frac{7}{2} m \]

5. **Solve for \( m \)**:
Now, we can solve for \( m \) by multiplying both sides by \( \frac{2}{7} \):
\[ m = \frac{2}{7} \]

6. **Convert to decimal**:
To express \( m \) in decimal form:
\[ m = \frac{2}{7} \approx 0.2857 \]

### Conclusion:
Thus, the value of \( n \) is \( 0.2857 \).