Step 1: Determine the atomic number of copper.
The atomic number of copper (Cu) is 29. This means a neutral copper atom has 29 electrons.
Step 2: Write the electron configuration for copper.
To write the electron configuration, we fill the orbitals according to the Aufbau principle, Hund's rule, and Pauli exclusion principle. However, copper is an exception to the strict Aufbau principle due to the stability associated with a completely filled d-subshell.
The expected configuration would be $[Ar]3d^9 4s^2$.
But to achieve extra stability, one electron from the $4s$ orbital moves to the $3d$ orbital, resulting in a completely filled $3d$ subshell.
Therefore, the actual ground state electron configuration of copper (Cu) is:
\[
\text{Cu: } [Ar]3d^{10}4s^1
\]
Step 3: Identify the number of unpaired electrons from the configuration.
Let us examine the orbitals:
The $3d$ subshell has 10 electrons ($3d^{10}$). A $d$-subshell has 5 orbitals. With 10 electrons, all five $d$ orbitals are completely filled, so there are no unpaired electrons in the $3d$ subshell.
The $4s$ subshell has 1 electron ($4s^1$). Since an $s$-subshell has one orbital, this electron remains unpaired.
Hence, total unpaired electrons:
\[
0 + 1 = 1
\]
Therefore, copper in its ground state has 1 unpaired electron.