For an ideal monoatomic gas, the universal gas constant R is n times the molar heat capacity a constant pressure `C_(p)`.Here n is

Options

A. `0.67`
B. `1.4`
C. `0.4`
D. `1.67`

Answer

To solve the problem, we need to find the value of \( n \) such that the universal gas constant \( R \) is \( n \) times the molar heat capacity at constant pressure \( C_p \) for an ideal monoatomic gas.

### Step-by-Step Solution:

1. **Understand the relationship**: We are given the equation:
\[ R = n \cdot C_p \]
where \( R \) is the universal gas constant and \( C_p \) is the molar heat capacity at constant pressure.

2. **Identify the value of \( C_p \)**: For an ideal monoatomic gas, the molar heat capacity at constant pressure \( C_p \) is given by:
\[ C_p = \frac{5}{2} R \]

3. **Substitute \( C_p \) into the equation**: Now, we can substitute the expression for \( C_p \) into the first equation:
\[ R = n \cdot \left(\frac{5}{2} R\right) \]

4. **Simplify the equation**: We can simplify this equation by dividing both sides by \( R \) (assuming \( R \neq 0 \)):
\[ 1 = n \cdot \frac{5}{2} \]

5. **Solve for \( n \)**: To find \( n \), we can rearrange the equation:
\[ n = \frac{2}{5} \]

6. **Convert to decimal**: The value of \( n \) can also be expressed as a decimal:
\[ n = 0.4 \]

### Final Answer:
Thus, the value of \( n \) is \( 0.4 \).

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