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)${\left(\frac{n_1{C}_1^2+n_2{C}_2^2+n_3{C}_1^3+\dots }{n_1+n_2+n_3+\dots }\right)}^{\frac{1}{2}}$
(b)$\frac{(n_1{C}_1^2+n_2{C}_2^2+n_3{C}_1^3+\dots {)}^{\frac{1}{2}}}{n_1+n_2+n_3+\dots }$
(c)$\frac{(n_1{C}_1^2{)}^{\frac{1}{2}}}{n_1}+\frac{(n_2{C}_2^2{)}^{\frac{1}{2}}}{n_2}+\frac{(n_3{C}_1^3{)}^{\frac{1}{2}}}{n_3}+\dots$
(d)${\left[\frac{(n_1{C}_1^2+n_2{C}_2^2+n_3{C}_1^3+\dots {]}^2}{(n_1+n_2+n_3+\dots )}\right]}^{\frac{1}{2}}$

• A. a
• B. b
• C. c
• D. d

Answer 1

The correct option is A a

Definition of RMS speed.