Final answer:
The statement is true; the average distance of an electron from the nucleus increases as the principal quantum number n increases, indicating higher energy levels and less electrostatic attraction.
Step-by-step explanation:
The statement that the possible state for an electron of an atom that is proportional to its distance to the nucleus is true. In the quantum mechanical model of the atom, the electron's energy levels are quantized and represented by the principal quantum number n. As n increases, the electron resides in higher energy levels and its average distance from the nucleus becomes greater. This is due to the inverse dependence of electrostatic attraction on distance. The lower the energy level (smaller n), the closer the electron is to the nucleus, as in the ground state where the electron is most tightly bound. In contrast, electrons in excited states with higher n values are found at greater distances from the nucleus and have higher energy, making the atom less stable.
Moreover, in the ground state of a hydrogen atom depicted by probability clouds, the likelihood of locating an electron is proportional to the darkness of the cloud, which indicates a higher probability area. These clouds show that while the electron can be closer or farther than the Bohr radius, it is improbable for it to be found at a significantly great distance from the nucleus.