For a free electron gas in two dimensions, derive the relation between the number density of electrons and the Fermi wave vector.

In two dimensions, the free electron gas can be described using the Fermi gas model. The electron energy depends only on its wavevector \( \vec{k} \), and the energy of an electron is given by:

\[
E(\vec{k}) = \frac{\hbar^2 k^2}{2m}
\]

where \( \hbar \) is the reduced Planck constant, \( k _____ __________ _________ _________ ________ _______ ______.
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