Question

At what temperature would hydrogen molecules (molecular mass is equal to (2.016 g/mol)) have an average velocity equal to the Moon's escape velocity of (2.38 km/s)?

a) (4.50 K)
b) (12.0 K)
c) (25.0 K)
d) (50.0 K)

Answer 1

The temperature at which hydrogen molecules have an average velocity equal to the Moon's escape velocity is 25.0 K.

Step-by-step explanation:

To find the temperature at which hydrogen molecules have an average velocity equal to the Moon's escape velocity, we can use the root-mean-square velocity formula:

Urms = sqrt(3KT/m)

Where Urms is the root-mean-square velocity, K is the Boltzmann constant, T is the temperature in Kelvin, and m is the molecular mass of the hydrogen molecule.

By rearranging the formula, we can solve for T:

T = (Urms^2 x m) / (3K)

Plugging in the values given:

T = ((2.38 km/s)^2 x 2.016 g/mol) / (3 x 1.38 x 10^-23 J/K)

Converting the units, we get:

T = 25.0 K