An alpha particle is fired directly toward a stationary gold nucleus from a very large distance where electrostatic potential energy is negligible, moving with an initial speed \(v_0\). Due to electrostatic repulsion, the alpha particle slows down as it approaches the nucleus, reaching a speed of \(\dfrac{1}{2}v_0\) at a distance \(d_0\) from the center of the nucleus. At what distance from the center of the nucleus will the speed of the alpha particle be \(\dfrac{1}{4}v_0\)?