For the given question above, there are other details that is missing. Here is what I got from my research.
Mass of a hydrogen atom as 1.008 u,
where 1 u=1.661 times 10^-27 kg.
The frequency of a mass on a spring is:
f = omega / 2pi = sqrt (k/meff) / 2pi
The meff you use is the effective mass. If two bodies with mass M and m are both free to move:
Meff = Mm / (M+m)
If M=m, then Meff = m/2 (as you were given)
So the answer is:
f = sqrt (2k/m) / 2pi
