Final answer:
The relative probability of finding an electron at a certain distance is depicted by the radial probability density, which peaks at the most probable radius and never reaches zero even at significant distances from the nucleus due to the quantum mechanical nature of electrons.
Step-by-step explanation:
The relative probability of finding an electron at a certain distance from the nucleus in an atom can be understood through the concept of radial probability density. This is quantified using the wavefunction squared (²), which indicates the likelihood of locating an electron at any point in space. For example, in the ground state of hydrogen, the electron density is highest around the nucleus, and the probability decreases steadily as the distance (r) increases. However, because the surface area of a spherical shell at radius r increases as 4πr², the actual radial probability (a product of probability density and surface area) will have a maximum value at some finite distance from the nucleus.
The most probable radius for finding an electron in the ground state of a hydrogen atom corresponds to the peak of this radial probability plot. It should be noted that while the electron density diminishes gradually with increasing distance, it never reaches zero, even at large distances from the nucleus. This reflects the quantum mechanical nature of electrons, which allows for a non-zero probability of finding the electron far from the nucleus.