Find the average momentum of molecules of hydrogen gas in a container at temperature `300K`.

Options

A. `2xxsqrt(900R)" g "cms^(-1)`
B. `1800" R g "cms^(-1)`
C. `sqrt(900R)" g "cms^(-1)`
D. zero

Answer

To find the average momentum of molecules of hydrogen gas in a container at a temperature of 300K, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
We have a container filled with hydrogen gas molecules. The temperature of the gas is given as 300K. At this temperature, the molecules are in constant random motion.

2. **Average Velocity of Molecules**:
In a gas, molecules move in random directions. When we calculate the average velocity of all the molecules, the contributions from molecules moving in opposite directions will cancel each other out. Therefore, the average velocity (\(V_{avg}\)) of the gas molecules can be considered as zero:
\[ V_{avg} = 0 \]

3. **Relation Between Momentum and Velocity**:
Momentum (\(P\)) of a molecule is given by the product of its mass (\(m\)) and its velocity (\(v\)):
\[ P = m \cdot v \]
The average momentum of the gas molecules is directly proportional to the average velocity.

4. **Calculating Average Momentum**:
Since we have established that the average velocity of the gas molecules is zero, we can conclude that the average momentum (\(P_{avg}\)) will also be zero:
\[ P_{avg} = m \cdot V_{avg} = m \cdot 0 = 0 \]

5. **Final Conclusion**:
Therefore, the average momentum of the hydrogen gas molecules in the container at 300K is:
\[ P_{avg} = 0 \]

### Final Answer:
The average momentum of hydrogen gas molecules at 300K is **zero**.

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