Answer:
v = 1247.92 m/s
Explanation:
The formula for kinetic energy is given as follows:
[tex]K.E = \frac{1}{2}mv^2[/tex]
Another formula that is used for Kinetic Energy is given as:
[tex]K.E = \frac{3}{2}KT[/tex]
Comparing both formulae for K.E:
[tex]\frac{1}{2}mv^2 = \frac{3}{2}KT\\\\mv^2 = 3KT\\v = \sqrt{ \frac{3KT}{m}}[/tex]
where,
v = rms speed of helium molecule = ?
K = Boltzmann Constant = 1.38 x 10⁻²³ J/k
T = Absolute Temperature = 250 K
m = mass of helium molecule = 6.646 x 10⁻²⁷ kg
Therefore,
[tex]v = \sqrt{\frac{(3)(1.38\ x\ 10^{-23}\ J/k)(250\ k)}{6.646\ x\ 10^{-27}\ kg}} \\\\[/tex]
v = 1247.92 m/s
