  In this article we propose a new relativistic paradox concerning the
absorption of a photon by a hydrogen atom. We show that the actual cause of the
paradox is one of the hypotheses of Bohr model; therefore, in order to solve
the paradox, we have to move away from Bohr model. Our analysis is carried out
only in the special relativistic framework, so we are not interested in giving
a full quantum mechanical treatment of the problem. We derive some expressions
for emission and absorption of photons by atoms, which are in perfect agreement
with special relativity, although comparable to the classical Bohr formula with
an excellent degree of approximation. Quite interestingly, these expressions
are no more invariant under a global shift of energy levels, showing a breaking
of classical "gauge invariance" of energy. We stress that, to the best of our
knowledge, the present approach has never been considered in literature. At the
end we will be able to solve the proposed paradox.
