Ratio of average kinetic energy of `H_2 and O_2` at a given temperature is

Options

A. ` 1: 16`
B. ` 1 : 8`
C. ` 1 : 4`
D. ` 1 :1 `

Explanation

To solve the problem of finding the ratio of average kinetic energy of \( H_2 \) and \( O_2 \) at a given temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Average Kinetic Energy**:
The average kinetic energy (\( KE \)) of a gas is given by the formula:
\[ KE = \frac{5}{2} RT \]
where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

2. **Identify the Gases**:
We are dealing with two diatomic gases: hydrogen (\( H_2 \)) and oxygen (\( O_2 \)).

3. **Apply the Formula**:
Since both gases are diatomic, we can use the same formula for both. Therefore, the average kinetic energy for \( H_2 \) is:
\[ KE_{H_2} = \frac{5}{2} RT \]
and for \( O_2 \):
\[ KE_{O_2} = \frac{5}{2} RT \]

4. **Calculate the Ratio**:
Now, we can find the ratio of the average kinetic energies of \( H_2 \) and \( O_2 \):
\[ \text{Ratio} = \frac{KE_{H_2}}{KE_{O_2}} = \frac{\frac{5}{2} RT}{\frac{5}{2} RT} = 1 \]

5. **Conclusion**:
The ratio of the average kinetic energy of \( H_2 \) to \( O_2 \) at a given temperature is:
\[ \text{Ratio} = 1:1 \]

### Final Answer:
The ratio of average kinetic energy of \( H_2 \) and \( O_2 \) at a given temperature is \( 1:1 \).

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