The average translational kinetic energy of O₂ (molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of N₂ (molar mass 28) molecules in eV at the same temperature is

The correct option is 0.048.

Step-by-Step Explanation:

According to the kinetic theory of gases, the average translational kinetic energy of a gas molecule is determined solely by its temperature. The formula is expressed as:

$E_t=\frac{3}{2}{k}_{B}T$

In this equation:

• 
  $k_B$ represents the Boltzmann constant.
  
• 
  $T$ represents the absolute temperature of the gas in Kelvin.
  

Key observations from this physical relation:

1. The average translational kinetic energy is directly proportional to the absolute temperature
$T$
.

2. The formula does not contain any term representing the mass or molar mass of the gas molecules. Therefore, at a specific temperature, all gas molecules (regardless of their mass) possess the exact same average translational kinetic energy.

Since the nitrogen (N₂) molecules are at the same temperature as the oxygen (O₂) molecules, their average translational kinetic energy must be identical, completely unaffected by the difference in their molar masses (28 g/mol versus 32 g/mol).

Given that the average translational kinetic energy of O₂ is 0.048 eV, the average translational kinetic energy of N₂ at the same temperature is also 0.048 eV.