I don't know if this is the way...but I kind of got the close answer....
we have d = 1.2 × 10^-10
r = d/2 = 0.6 × 10 ^-10
v = 460
3 × rotational KE = 2 × translational KE
(3 . I . w^2 ) / 2 = (2 . m . v^2) / 2
3 . m . r^2 . w^2 = 2 . m . v^2
w^2 = (2/3) . v^2/r^2
w = ✓(2/3) . v/r
w = ✓(2/3) ...