The speeds of 5 molecules of a gas (in arbitrary units) are as follows : 2, 3, 4, 5, 6. The root mean square speed for these molecules is

The correct option is 4.24.

To find the root mean square (rms) speed of the molecules, we follow a step-by-step process: squaring the individual speeds, taking their average (mean), and then taking the square root of that average.

Step 1: Identify the given speeds of the molecules
The speeds of the 5 molecules are:

$v_1=2$

$v_2=3$

$v_3=4$

$v_4=5$

$v_5=6$

The total number of molecules,
$N=5$.

Step 2: Calculate the square of each individual speed
Now, we square each speed value:

$v_1^2=2^2=4$

$v_2^2=3^2=9$

$v_3^2=4^2=16$

$v_4^2=5^2=25$

$v_5^2=6^2=36$

Step 3: Calculate the mean (average) of these squared values
We sum the squared values and divide by the total number of molecules:

$\text{Mean of squares}=\frac{4+9+16+25+36}{5}$

$\text{Mean of squares}=\frac{90}{5}=18$

Step 4: Calculate the square root of the mean
To obtain the root mean square speed (
$v_{\text{rms}}$
), we take the square root of the mean of squares calculated in Step 3:

$v_{\text{rms}}=\sqrt{18}$

$v_{\text{rms}}\approx 4.24$

Thus, the root mean square speed of the molecules is 4.24 arbitrary units.