Question

At a certain temperature, the average kinetic energy of a hydrogen molecule is

6.2×10^−21 J. If the mass of the hydrogen molecule is 3.1×10−27 kg, find:

The temperature The root mean square velocity of the hydrogen molecule
a. T=300K,v rms=1.26×10^3 m/s
b. T=600K,vrms =1.26×10^3m/s
c. T=300K,vrms=2.52×10^3m/s
d. T=600K,v rms=2.52×10^3m/s

Answer 1

The temperature of the hydrogen molecule is 300K, and the root mean square velocity is 1.26×10^3 m/s.

Step-by-step explanation:

The average kinetic energy of a molecule is related to its temperature by the equation KE = (3/2)kT, where KE is the average kinetic energy, k is the Boltzmann constant (1.38×10^-23 J/K), and T is the temperature in Kelvin.

To find the temperature, we can rearrange the equation to T = (2/3)(KE/k). Plugging in the given value for the average kinetic energy of the hydrogen molecule (6.2×10^-21 J) and the mass of the hydrogen molecule (3.1×10^-27 kg), we can calculate the temperature to be 300K.

To find the root mean square velocity (vrms) of the hydrogen molecule, we can use the equation vrms = sqrt((3kT)/m), where m is the mass of the molecule.

Plugging in the calculated temperature (300K) and the given mass of the hydrogen molecule (3.1×10^-27 kg), we can calculate the root mean square velocity to be 1.26×10^3 m/s.