Two flasks `A` and `B` of equal volume are at temperature `100 K` and `200 K` containing `H_(2)` and `CH_(4)`, respectively. Which of the following is true about `KE` per mole (`KE=` Kinetic energy).

Options

A. `KE` per mole of `H_(2)` is twice that of `CH_(4)`
B. `KE` per mole of `CH_(4)` is twice that of `H_(2)`
C. `KE` per mole of `H_(2)` is equal to that of `CH_(4)`
D. `KE` per mole of `CH_(4)` is thrice that of `H_(2)`

Explanation

To determine the kinetic energy per mole of hydrogen (H₂) in flask A at 100 K and methane (CH₄) in flask B at 200 K, we can use the formula for kinetic energy per mole derived from the kinetic theory of gases:

### Step-by-Step Solution:

1. **Understanding the Relationship**: According to the kinetic theory of gases, the kinetic energy (KE) per mole of a gas is directly proportional to its absolute temperature (T). The formula is given by:
\[ KE = \frac{3}{2}RT \]
...