Question

the most probable speed of atoms of argon (at weight = 40) at 27 °C (in m/s) is
a. ~420 m/s
b. ~350 m/s

Answer 1

The temperature of a gas is the measure of the average kinetic energy of the gas, and from the kinetic energy we can calculate the speed. The most probable speed will be determined by a Maxwell Boltzman distribution thus and is given by

\[v_p=\sqrt{\frac{2kT}{m}}\]

Plugging the numbers in (remembering to use thermodynamic temperature such that 27 C = 300 K) we get \[v=\sqrt{\frac{(2)\times(1.38\times10^{-23})\times(300)}{(40\times1.66\times10^{-27})}}\] and we get \(v=353\) m/s. So your answer would be a, it is about 350 m/s.

See here fro an explanation of where this comes from http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html in particular the Maxwell speed distribution (below which you will see a speed calculator to help you calculate the various speeds)

Answer 2

Sorry bit of a confusion in the post. the answer is b. ~350 m/s. i stated above the answer was a. 350 m/s. I just wanted to be clear (in case of confusion) that the answer is indeed b. ~350 m/s.

Answer 3

tnx a lot ... :)