Which of the following systems will have the larger ionization energy? Explain your reasoning. i) an electron at a distance \(d_{1}\) from a nucleus with charge \(+2\) ii) an electron at a distance \(d_{1}\) from a nucleus with charge \(+1\)

The relationship between an electron and the nucleus is fundamental in understanding chemical properties. The nucleus, packed with protons, harbors a positive charge, while an electron carries a negative charge. According to Coulomb's Law, opposite charges attract each other, meaning there's a force that pulls electrons towards the nucleus.

This force of attraction depends on two primary factors: the charge of the nucleus (number of protons) and the distance of the electron from the nucleus. A larger positive charge on the nucleus or a smaller distance to the electron will result in a stronger attraction. Conversely, a smaller charge or a greater distance means a weaker attraction. This concept is crucial in explaining why system i, with its higher nuclear charge of +2, would have a stronger electron-nucleus attraction compared to system ii, with a charge of +1.

Atomic charge refers to the effective nuclear charge that an electron experiences in an atom. This is not just the actual charge of the nucleus (determined by the number of protons), but also includes the screening effect of other electrons that might be between the nucleus and the electron of interest.

The atomic charge is pivotal in determining the chemical behaviour of an element. Elements with higher effective nuclear charges are likely to hold their electrons more tightly, making them less reactive, whereas elements with lower effective nuclear charges will have electrons that are more easily influenced by external forces. This detail assists in understanding why an electron in system i, with a nucleus that has a +2 charge, experiences a greater effective atomic charge compared to an electron in system ii.

Removal of an electron from its orbital, also known as ionization, requires a precise amount of energy, called the ionization energy. This process is central to many reactions in chemistry, where electrons are transferred between atoms and molecules.

Ionization energy is influenced by the electron-nucleus attraction because a strong attraction means the electron is more tightly bound to the nucleus, thus requiring more energy to be removed. This concept supports the conclusion that the ionization energy for system i is greater, since its +2 nuclear charge binds the electron more firmly than the +1 charge in system ii, meaning more energy is needed to ionize the electron.