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In the present work we study the effect of unparticle modified static potentials on the energy levels of the hydrogen atom. By using Rayleigh–Schrödinger perturbation theory, we obtain the energy shift of the ground state and compare it with experimental data. Bounds on the unparticle energy scale U as a function of the scaling dimension and the coupling constant λ are derived. We show that there exists a parameter region where bounds on U ar are stringent, signaling that unparticles could be tested in atomic physics experiments.