Assertion : The ratio `C_(P)//C_(upsilon)` is more for helium gas than for hydrogen gas.
Reason : Atomic mass of helium is more than that of hydrogen.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

To solve the given question, we will analyze the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states that the ratio \( \frac{C_p}{C_v} \) (denoted as \( \gamma \)) is more for helium gas than for hydrogen gas.

### Step 2: Identifying the Type of Gases
- Helium is a **monatomic gas**.
- Hydrogen (H₂) is a **diatomic gas**.

### Step 3: Degrees of Freedom
The degrees of freedom for gases are as follows:
- For a monatomic gas (like helium), the degrees of freedom \( f = 3 \) (only translational motion).
- For a diatomic gas (like hydrogen), the degrees of freedom \( f = 5 \) (3 translational and 2 rotational).

### Step 4: Calculating \( \gamma \) for Each Gas
Using the formula for \( \gamma \):
\[ \gamma = \frac{C_p}{C_v} = \frac{f + 2}{f} \]

- For helium (monatomic):
\[ \gamma_{He} = \frac{3 + 2}{3} = \frac{5}{3} \]

- For hydrogen (diatomic):
\[ \gamma_{H_2} = \frac{5 + 2}{5} = \frac{7}{5} \]

### Step 5: Comparing the Values of \( \gamma \)
Now we compare the two values:
- \( \frac{5}{3} \) (for helium) and \( \frac{7}{5} \) (for hydrogen).

To compare these fractions, we can convert them to a common denominator or convert them to decimal:
- \( \frac{5}{3} \approx 1.67 \)
- \( \frac{7}{5} = 1.4 \)

Since \( 1.67 > 1.4 \), we conclude that:
\[ \gamma_{He} > \gamma_{H_2} \]

### Step 6: Conclusion on the Assertion
Thus, the assertion is **true**: the ratio \( \frac{C_p}{C_v} \) is indeed more for helium gas than for hydrogen gas.

### Step 7: Analyzing the Reason
The reason states that the atomic mass of helium is more than that of hydrogen. While this statement is true, it does not explain why \( \gamma \) for helium is greater than that for hydrogen. The ratio \( \frac{C_p}{C_v} \) depends on the degrees of freedom, not the atomic mass.

### Final Conclusion
- The assertion is true.
- The reason is true, but it is **not the correct explanation** for the assertion.

### Final Answer
The correct answer is: **Assertion is true, Reason is true, but Reason is not the correct explanation for Assertion.**

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