Question

The outermost valence electron in atom A experiences an effective nuclear charge of \(2+\) and is on average 225 pm from the nucleus. The outermost valence electron in atom B experiences an effective nuclear charge of \(1+\) and is on average 175 pm from the nucleus. Which atom (A or B) has the higher first ionization energy? Explain.

Short answer

Atom A has the higher first ionization energy due to its higher effective nuclear charge of \(2+\), despite being farther from the nucleus compared to atom B's \(1+\) effective nuclear charge.

Step-by-step solution

Understand Ionization Energy

Ionization energy is the amount of energy required to remove an electron from an atom. A higher effective nuclear charge typically increases the ionization energy because the increased positive charge in the nucleus attracts electrons more strongly. Additionally, the farther an electron is from the nucleus, the lower the ionization energy, because the attraction between the nucleus and the electron is weaker at greater distances.

Evaluate Effective Nuclear Charge

Compare the effective nuclear charges experienced by the valence electrons in atoms A and B. Atom A's valence electron feels an effective nuclear charge of \(2+\), while atom B's valence electron feels a charge of \(1+\). The greater the effective nuclear charge, the greater the pull on the electron and the higher the ionization energy.

Consider Average Distance from Nucleus

Assess the average distances of the valence electrons from their respective nuclei. Atom A has its valence electron on average 225 pm away, while atom B's valence electron is on average 175 pm away from the nucleus. A greater distance implies a weaker attraction and, therefore, a lower ionization energy.

Compare Ionization Energies

Weigh the effects of both the effective nuclear charge and the distance from the nucleus. Although atom B’s electron is closer to the nucleus, which would suggest a higher ionization energy, the effective nuclear charge is lower for atom B (\(1+\)) compared to atom A (\(2+\)). The effective nuclear charge has a more significant influence in this case.

Conclude Which Atom Has a Higher First Ionization Energy

Considering both factors, the higher effective nuclear charge in atom A suggests its valence electron is held more tightly than in atom B, even though it is farther from the nucleus. Thus, atom A will have a higher first ionization energy than atom B.

Key concepts

Effective Nuclear Charge

The concept of effective nuclear charge (ENC) is crucial in understanding how atoms hold onto their electrons. ENC refers to the net positive charge experienced by an electron in an atom. This is not simply the total positive charge of the protons in the nucleus; it's reduced by the shielding effect of other electrons, particularly those in inner shells, which block some of the nuclear charge from affecting the outer electrons.

Higher ENC means that the valence electrons feel a stronger pull towards the nucleus, as there is less shielding by other electrons. The ENC is a vital factor in determining the ionization energy, which is the energy required to remove an electron from an atom. In the exercise, atom A has an ENC of 2+, which suggests it has a higher ionization energy, because with a stronger effective nuclear charge, its electrons are more tightly bound to the nucleus compared to atom B, which has an ENC of 1+.

Valence Electrons

Valence electrons are the electrons in the outermost shell of an atom and play a significant role in chemical bonding and reactivity. These electrons are the ones involved in forming chemical bonds with other atoms. The ease with which an atom can gain, lose, or share electrons largely depends on the interaction between the valence electrons and the nucleus, specifically the strength of the attraction they feel from the nucleus - in other words, the effective nuclear charge.

When the ENC is high, valence electrons are held more closely, making an atom less likely to lose an electron and thus resulting in a higher ionization energy. From the exercise, we know that the valence electron of atom A experiences a stronger ENC than atom B, which implies that atom A has valence electrons that are more tightly bound to the nucleus and thus harder to remove.

Periodic Trends in Ionization Energy

Ionization energy exhibits distinct trends within the periodic table. Generally, ionization energy increases across a period from left to right due to increased effective nuclear charge as protons are added to the nucleus without additional shielding. Conversely, ionization energy decreases down a group because valence electrons are at higher energy levels, farther from the nucleus, and more shielded by inner electron shells.

The interplay between distance from the nucleus and ENC results in these periodic trends. Even though atom B's valence electron is closer to its nucleus, atom A's valence electron feels a stronger ENC. As per periodic trends, the attraction to the nucleus (and thus ionization energy) is stronger in atom A despite the greater distance because of the higher ENC. This demonstrates how effective nuclear charge plays a more dominant role in ionization energy than the mere distance of the valence electron from the nucleus.