Molecular speeds: What is the root-mean-square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?
A) 5.4 m/s
B) 1.9 m/s
C) 3.1 m/s
D) 3.3 m/s
E) 1.0 m/s

Question

Quizplus · Accepted Answer

The root-mean-square (rms) velocity is given by the formula:

vrms = sqrt((v1^2 + v2^2 + v3^2 + ... + vn^2)/n)

where n is the number of velocity components.

Using the given velocity components, we have:

vrms = sqrt((2.0^2 + (-3.0)^2 + 4.0^2) / 3) 
     = sqrt((4.0 + 9.0 + 16.0) / 3)
     = sqrt(29.0 / 3)
     ≈ 3.1 m/s

Therefore, the best choice is C, with an rms velocity of 3.1 m/s.

Molecular Speeds: What Is the Root-Mean-Square Value of the Following