Question

If $C_1,C_2,C_3$.........represent the speeds of $n_1,n_2,n_3$......... molecules, then the root mean square speed is _____.

• A. $\frac{\sqrt{n_1{C_1}^2+n_2{C_2}^2+n_3{C_3}^2+...}}{n_1+n_2+n_3+...}$
• B. $\frac{{⟮n_1{C_1}^2+n_2{C_2}^2+n_3{C_3}^2+..⟯}^{\frac{1}{2}}}{n_1+n_2+n_3+.....}$
• C. $\frac{{⟮n_1{C_1}^2⟯}^{\frac{1}{2}}}{n_1}+\frac{{⟮n_2{C_2}^2⟯}^{\frac{1}{2}}}{n_2}+\frac{{⟮n_3{C_3}^2⟯}^{\frac{1}{2}}}{n_3}+.....$
• D. $⟮\frac{{⟮n_1{C}_1+n_2{C}_2+n_3{C}_3+...⟯}^2}{⟮n_1+n_2+n_3+.....⟯}{⟯}^{\frac{1}{2}}$

Answer 1

The correct option is A

$\frac{\sqrt{n_1{C_1}^2+n_2{C_2}^2+n_3{C_3}^2+...}}{n_1+n_2+n_3+...}$

Root mean square speed = $\frac{\sqrt{n_1{C_1}^2+n_2{C_2}^2+n_3{C_3}^2+...}}{n_1+n_2+n_3+...}$