The rms speed of oxygen molecules in a gas is v. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become
Root mean square velocity of gas is given as
vrms 
where R=gas constant whose value is 8.31 J/mol K.
T=temperature of gas.
M= molar mass of molecule of gas
Given,
Root mean square of oxygen
vrms 
Molar mass of oxygen molecule M=32. So,
When temperature is doubled, oxygen molecule dissociates into oxygen atom.
Molar mass of oxygen atom M’=16
New temperature T’=2T
Then rms speed of oxygen atom becomes
Multiplying and diving above equation by 2 we get,
New rms speed of oxygen will ve 2v.
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