The root-mean-square (rms) speed of oxygen molecules `(O_(2))` at a certain absolute temperature is v.If the temperature is double and the oxygen gas dissociated into atomic oxygen, the rms speed would be

Options

A. v
B. `sqrt2 v`
C. `2v`
D. `2 sqrt2 v`

Answer

C

Explanation

RMS speed is given by
`v _(rms) = v = sqrt ((3 RT)/( M ))`
New temperature `T . = 2T`
New molar mass `M . = (M)/(2)`
`therefore ( v _(rms)) _("new") = sqrt ((3 R (2T))/( ( ( M )/(2))))`
`( v _(rms)) _("new") = 2 v `