You are given the following group of particles `n_(1)` represents the number of molecules with speed `upsilone_(1)`

Answer

`3.17 ms^(-1), 3.36 ms^(-1)`, `3.0 ms^(-1)`

Explanation

(i) The average speed is
`upsilon_(av) = (n_(1)upsilon_(1)+n_(2)upsilon_(2)+n_(3)upsilon_(3)+n_(4)upsilon_(4)+n_(5)upsilon_(5))/((n_(1)+n_(2)+n_(3)+n_(4)+n_(5)))`
`=(2 xx 1 +4 xx 2 + 8 xx 3 +6 xx 4 +3 xx 5)/((2+4+8+6+3)) = 73/223`
`=3.17 ms^(-1)` (ii) The root mean square speed is ,
`upsilon_(rms) = ((n_(1)upsilon_(1)^(2)+n_(2)upsilon_(2)^(2)+n_(3)upsilon_(3)^(3)+n_(4)upsilon_(4)^(2)+n_(5)upsilon_(5)^(2))/(n_(1)+n_(2)+n_(3)+n_(4)+n_(5)))^(1//2)`
`=((2 xx 1^(2) +4 xx 2^(2) + 8 xx 3^(2) +6 xx 4^(2) +3 xx 5^(2))/(2+4+8+6+3))^(1//2)`
`=3.36 ms^(-1)`
(iii) The most probable speed is that speed which is possessed by maximum number of particles, Accordingly , most probable speed = `3.0 ms^(-1)`