  In this paper we present exact solutions of the Dirac equation on the
non-commutative plane in the presence of crossed electric and magnetic fields.
In the standard commutative plane such a system is known to exhibit contraction
of Landau levels when the electric field approaches a critical value. In the
present case we find exact solutions in terms of the non-commutative parameters
$\eta$ (momentum non-commutativity) and $\theta$ (coordinate non-commutativity)
and provide an explicit expression for the Landau levels. We show that
non-commutativity preserves the collapse of the spectrum. We provide a dual
description of the system: (i) one in which at a given electric field the
magnetic field is varied and the other (ii) in which at a given magnetic field
the electric field is varied. In the former case we find that momentum
non-commutativity ($\eta$) splits the critical magnetic field into two critical
fields while coordinates non-commutativity ($\theta$) gives rise to two
additional critical points not at all present in the commutative scenario.
