Eleven molecules have speeds 16,17,18,...,26 m/s.Calculate the root-mean-square of this group of molecules.
A) 21.2 m/s
B) 21.0 m/s
C) 21.5 m/s
D) 21.7 m/s

Question

Quizplus · Accepted Answer

The root-mean-square speed ($v_{rms}$) is calculated using the formula: $v_{rms} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}v_i^2}$, where $v_i$ are the individual speeds and $n$ is the number of molecules. For speeds 16 to 26 m/s, we first calculate the sum of the squares of these speeds and then divide by the number of speeds (11) before taking the square root. The calculation is as follows: $\sum_{i=16}^{26}i^2 = 16^2 + 17^2 + ... + 26^2 = 3916$, and $n = 11$. Thus, $v_{rms} = \sqrt{\frac{3916}{11}} \approx 21.2$ m/s.

Eleven Molecules Have Speeds 16,17,18