In a gaseous mixture of massive molecules and light molecules with the same average KE, which have the greater speed?
A. the massive molecules
B. the light molecules
C. Cannot be determined
D. They have the same speed.
Kinetic energy of any object is given by the formula:
kinetic energy = k = (m*v^2)/2
Where: m = mass and v = speed of the object.
In the question the let us say: average mass of massive molecules is m1 and speed is v1.
Similarly, average mass of light molecules ball is m2 and speed is v2.
It is given then kinetic energy of both the massive and light molecules is same.
Therefore: (m1*v1^2)/2 = (m2*v2^2)/2
Therefore: m1*v1 = m2*v2
We know that massive molecules are heavier than lighter molecules. Therefore
And if m1*v1 = m2*v2
Therefore, lighter molecules heavy greater speed.
Thus alternative B) is right.