The root mean square velocity of gas molecules as a function of temperature is (M is molecular weight):
v²rms = 3RT/M,
and kinetic energy is given by:
KE = ½Mv ²
We can make the substitution:
KE = ½M3RT/M, or
KE = (3/2)RT.
Notice the molecular weight variable is gone; that means the answer will be the same for F2, Cl2, and Br2:
KE = (3/2) (8.314 J/K*mole) (290 K) = 3617 J/mole.