The drift velocity $v_d$ can be found using the formula for current $I$ in a conductor:

$I = nqAv_d$,

where:

• $n$ is the number density of free electrons (number of free electrons per unit volume),
• $q$ is the charge of an electron,
• $A$ is the cross-sectional area of the conductor, and
• $v_d$ is the drift velocity of the electrons.

We can rearrange the above formula to solve for $v_d$:

$v_d = \frac{I}{nqA}$.

Given that $I = 2 \, \text{A}$, $n = 2.0 \times 10^{28} \, \text{m}^{-3}$, $q = 1.6 \times 10^{-19} \, \text{C}$, and $A = 25.0 \, \text{mm}^{2} = 25.0 \times 10^{-6} \, \text{m}^{2}$, we can substitute these values into the formula to find $v_d$:

$v_d = \frac{2}{(2.0 \times 10^{28})(1.6 \times 10^{-19})(25.0 \times 10^{-6})}$

$v_d = 25 \times 10^{-6} \, \text{ms}^{-1}$.

Therefore, the drift velocity of the electrons is $25 \times 10^{-6} \, \text{ms}^{-1}$.