Two equal volume flasks cotaining equal masses of `H_(2)` and `CH_(4)` are at `100 K` and `200 K`, respectively. The molecular diameter of `CH_(4)` is twice that of `H_(2)`. Which of the following statement about `Z_(1)` (number of collisions per molecule per `cm^(3)` per second) is true? (`a`) `Z_(11)` of `H_(2)=2Z_(1)` of `CH_(4)`
(`b`) `Z_(11)` of `H_(2)=4Z_(1)` of `CH_(4)`
(`c`) `Z_(11)` of `H_(2)=Z_(1)` of `CH_(4)`
(`d`) `Z_(11)` of `H_(2)=8Z_(1)` of `CH_(4)`

Explanation

To solve the problem, we will analyze the collision frequency \( Z \) for both gases \( H_2 \) and \( CH_4 \) using the formula for collision frequency and the given parameters.

### Step 1: Understand the formula for collision frequency
The collision frequency \( Z \) is given by the formula:
\[ Z = \frac{\pi}{\sqrt{2}} n v \sigma u_{\text{avg}} \]
where:
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