An electron in a hydrogen atom has a total energy of -3.4 eV. If...

The kinetic energy $K$ of an electron is equal to the magnitude of its total energy $E$.
$K = |E| = 3.4 \text{ eV}$

Converting this to Joules:
$K = 3.4 \times 1.6 \times 10^{-19} \text{ J} = 5.44 \times 10^{-19} \text{ J}$

The centripetal force $F_c$ is provided by the electrostatic force, and is related to kinetic energy as:
$F_c = \dfrac{mv^2}{r}$

Since $K = \dfrac{1}{2}mv^2$, we can write $mv^2 = 2K$.
Substituting this into the force equation gives:
$F_c = \dfrac{2K}{r}$

Rearranging for the radial distance $r$:
$r = \dfrac{2K}{F_c}$

Substituting the given values:
$r = \dfrac{2 \times 5.44 \times 10^{-19}}{5.1 \times 10^{-9}}$

$r = \dfrac{10.88 \times 10^{-19}}{5.1 \times 10^{-9}} \approx 2.13 \times 10^{-10} \text{ m}$

This is approximately $2.1 \times 10^{-10}$ m.

Answer: $2.1 \times 10^{-10}$ m