Question

Five molecules have the following speeds in m s^-1: 473, 482, 517, 490, 501.

Calculate their root mean square speed.

Answer 1

By definition, the root mean square speed is (see https://en.wikipedia.org/wiki/Root_mean_square):

$$v_{RMS} = \sqrt{ \frac{1}{n} \left( v_1^2 + v_2^2 + \cdots + v_n^2 \right) }$$

where $v_i$ are individual speeds, and $n$ is the number of given speeds. In our case $n = 5$, thus, have:

$$v_{RMS} = \sqrt{ \frac{1}{5} \left( 473^2 + 482^2 + 517^2 +490^2 + 501^2 \right) } \approx 492.84m/s$$

Answer. 492.84 m/s.