Average atomic mass argon

The isotopes of argon have the following relative abundances Ar-36, 0.34% Ar-38, 0.06% and Ar-40, 99.66%. Estimate the average atomic mass of argon. 

As discussed in the chapter, the atomic mass of argon is greater than that of potassium. This observation created a problem in the early development of the periodic table because it meant that argon should be placed after potassium, (a) How was this difficulty resolved (b) From the following data, calculate the average atomic masses of argon and potassium Ar-36 (35.9675 amu, 0.337 percent), Ar-38 (37.9627 amu, 0.063 percent), Ar-40 (39.9624 amu, 99.60 percent), K-39 (38.9637 amu, 93.258 percent). K-40 (39.9640 amu. 0.0117 percent). K-41 (40.9618 amu, 6.730 percent). 

The atomic weight of an element is a weighted average of the mass of the naturally occurring isotopes of that element. Therefore, the atoms in a naturally occurring sample of argon must be heavier than the atoms in a naturally occurring sample of potassium. 

Consider a system of I f spherical atoms (such as those of argon), each having a mass m and some velocity v,. The atomic velocities differ, but we can form an average velocity (which would be zero for a static system) and an average molecular kinetic energy (which is always greater than zero). 

---