Question

Nitrogen molecules in the atmosphere of the earth have a root mean square speed of 410 m s¹. the molar masses of nitrogen and helium are 28 g mol and 4 g mol¹ respectively. calculate the root mean square speed of the helium molecules in the atmosphere.

Answer 1

The root mean square speed of helium molecules in the atmosphere can be calculated using the molar mass of helium and the given root mean square speed of nitrogen molecules. The calculation involves using the formula for root mean square speed and solving for temperature.

Step-by-step explanation:

The root mean square speed of molecules can be calculated using the equation:

Urms = sqrt((3kT)/m)

Where Urms is the root mean square speed, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the molar mass of the molecule. In this case, we are given that the root mean square speed of nitrogen molecules is 410 m/s and the molar mass of nitrogen is 28 g/mol. To find the root mean square speed of helium molecules, we can use the same equation with the molar mass of helium (4 g/mol) and solve for T:

T = (Urms^2 * m) / (3k)

Substituting the given values:

T = (410^2 * 4) / (3 * 1.38 * 10^-23)

Calculating this gives us T = 3250 K. Therefore, the root mean square speed of helium molecules in the atmosphere is approximately 3250 K.