If the average kinetic energy of a molecule of hydrogen gas at 300 K is E , then the average kinetic energy of a molecule of nitrogen gas at the same temperature is

Options

A. 7E
B. 14E
C. `(E )/(7)`
D. E

Answer

To solve the problem, we need to understand the relationship between the average kinetic energy of gas molecules and temperature. The average kinetic energy of a molecule of an ideal gas is given by the formula:

\[ E = \frac{3}{2} k T \]

where:
- \(E\) is the average kinetic energy,
- \(k\) is the Boltzmann constant,
- \(T\) is the absolute temperature in Kelvin.

1. **Identify the given information**:
- The average kinetic energy of a hydrogen gas molecule at 300 K is given as \(E\).

2. **Understand the formula**:
- The average kinetic energy of a gas molecule is directly proportional to the absolute temperature \(T\). This means that if the temperature remains constant, the average kinetic energy will also remain constant regardless of the type of gas.

3. **Apply the formula for nitrogen gas**:
- Since the temperature for nitrogen gas is also 300 K, we can use the same formula to find its average kinetic energy. The average kinetic energy for nitrogen gas at 300 K will also be:

\[ E_{N_2} = \frac{3}{2} k T \]

4. **Compare the two gases**:
- Since both hydrogen and nitrogen are at the same temperature (300 K), their average kinetic energies will be equal. Therefore, the average kinetic energy of a nitrogen molecule at 300 K is also \(E\).

5. **Conclusion**:
- The average kinetic energy of a molecule of nitrogen gas at 300 K is also \(E\).

Thus, the answer is:

\[ \text{Average kinetic energy of nitrogen gas at 300 K} = E \]