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 (KE) of a molecule of an ideal gas is given by the formula:

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

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

Given that the average kinetic energy of a molecule of hydrogen gas at 300 K is \( E \), we can express this as:

\[ E = \frac{3}{2} k (300) \]

Now, we need to find the average kinetic energy of a molecule of nitrogen gas at the same temperature (300 K). Since the formula for average kinetic energy depends only on temperature and not on the type of gas, we can conclude that:

\[ KE_{\text{nitrogen}} = \frac{3}{2} k (300) \]

Since both gases are at the same temperature, the average kinetic energy of nitrogen gas will also be:

\[ KE_{\text{nitrogen}} = E \]

Thus, the average kinetic energy of a molecule of nitrogen gas at 300 K is also \( E \).

### Final Answer:
The average kinetic energy of a molecule of nitrogen gas at the same temperature (300 K) is \( E \).