Final answer:
The temperature of a gas sample can be calculated from the average translational kinetic energy of a molecule using the equation KE = (3/2)kT, where k is the Boltzmann constant. By rearranging the equation, one can find the temperature in Kelvin.
Step-by-step explanation:
The question is asking about the relationship between the average translational kinetic energy of a gas molecule and the temperature of the sample of gas. The equation that relates these two quantities is given by the expression for the average kinetic energy of a particle in a gas, which is KE = (3/2)kT, where k is the Boltzmann constant (1.38 × 10-23 J/K), and T is the temperature in Kelvin. Given that the average translational kinetic energy (KE) is 8.53× 10^-21 J, we can rearrange the equation to solve for T: T = (2/3)(KE/k).