  In the present work we study the effect of unparticle modified static
potentials on the energy levels of the hydrogen atom. By using
Rayleigh-Schr\"odinger perturbation theory, we obtain the energy shift of the
ground state and we compare it with experimental data. Bounds on the unparticle
energy scale $\Lambda_\mathcal{U}$ as a function of the scaling dimension
$d_\mathcal{U}$ and the coupling constant $\lambda$ are derived. We show that
there exists a parameter region where bounds on $\Lambda_\mathcal{U}$ are
stringent, signalling that unparticles could be tested in atomic physics
experiments.
