Four molecules of a gas have speeds 1,2,3 and 4km/s. The value of the root mean square speed of the gas molecules is-

Root mean square (RMS) speed নির্ণয়:

\(v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + v_4^2}{N}}\) 🧐

এখানে,

\(v_1 = 1\) km/s,

\(v_2 = 2\) km/s,

\(v_3 = 3\) km/s,

\(v_4 = 4\) km/s,

\(N = 4\) (মোট অণুর সংখ্যা) 😮

অতএব,

\(v_{rms} = \sqrt{\frac{1^2 + 2^2 + 3^2 + 4^2}{4}}\) km/s 😎

\(= \sqrt{\frac{1 + 4 + 9 + 16}{4}}\) km/s 😊

\(= \sqrt{\frac{30}{4}}\) km/s 🤔

\(= \sqrt{\frac{15}{2}}\) km/s 🤩

\(= \sqrt{\frac{15 \times 2}{2 \times 2}}\) km/s 🤓

\(= \sqrt{\frac{30}{4}}\) km/s 🥳

\(= \frac{\sqrt{30}}{2}\) km/s 👍

সুতরাং, RMS speed হলো \( \frac{1}{2}\sqrt{30} \) km/s। 🥳