Question

Four molecules of a gas are having speeds 1, 4, 8 and 16 ms⁻¹. The root mean square velocity of the gas molecules is:

A 7.25 ms⁻¹
B 52.56 ms⁻¹
C 84.25 ms ⁻¹
D 9.2 ms ⁻¹

Answer 1

To find the root mean square velocity, we square each speed, calculate their average, and take the square root of this average. The rms velocity for the given speeds 1, 4, 8, and 16 m/s is approximately 9.2 m/s, corresponding to option D.

Step-by-step explanation:

The question is asking to calculate the root mean square (rms) velocity of gas molecules given their individual speeds. To find this, we use the formula for rms speed which is the square root of the average of the squares of the individual speeds. Therefore, we need to square each speed, calculate their average, and then take the square root of this average.

The speeds given are 1, 4, 8, and 16 m/s. First, we square these speeds:

• 12 = 1
• 42 = 16
• 82 = 64
• 162 = 256

Now, calculate the average of these squared values:

(1 + 16 + 64 + 256) / 4 = 337 / 4 = 84.25

Finally, we take the square root of the average:

sqrt(84.25) ≈ 9.2 ms−1

Therefore, the root mean square velocity of the gas molecules is 9.2 m/s, which corresponds to option D.