Question

As the nuclear charge increases from neon to calcium, the orbital energies: (a) Increase very slow (b) Increase very rapidly (c) Fall (d) Increase

Short answer

(c) Fall

Step-by-step solution

Understand the concept of nuclear charge

Nuclear charge is the positive charge of the nucleus equal to the number of protons in the nucleus. As we move across a period in the periodic table, additional protons are added to the nucleus, which increases the nuclear charge.

Recognize the effect of nuclear charge on orbital energies

An increase in nuclear charge increases the attractive force between the nucleus and the electrons. This results in the reduction of energy of the orbitals, making them more stable and thus causing them to fall in energy.

Apply the concept to the period from neon to calcium

Neon and calcium belong to different periods, but as you move across a period from neon to calcium, the nuclear charge increases gradually. This increase typically leads to a decrease in the energy of the orbitals due to the stronger attractive forces.

Conclusion about the change in orbital energies

As nuclear charge increases, orbital energies generally fall, because the electrons are held more tightly by the nucleus. Thus, energy levels of the orbitals become lower.

Key concepts

Orbital Energies

In the context of nuclear chemistry, understanding orbital energies is crucial to comprehending the behavior of electrons within an atom. Orbital energies are the energy levels within which electrons reside. As electrons orbit the nucleus, they do so in specific shells or orbitals, each with a defined energy level. The term "orbital energy" refers to the potential energy of electrons bound to their respective orbitals under the influence of the nucleus's positively charged protons.
When nuclear charge increases, which occurs when moving towards elements with higher atomic numbers, the added protons create a stronger positive charge at the nucleus. This increase in positive charge enhances the attraction between the nucleus and electrons and thus pulls the electrons closer. As a result, the orbital energies decrease because electrons are attracted more strongly and become more tightly bound to the nucleus. This makes the orbitals more stable and lowers their energy. Therefore, even though more energy is generally associated with moving electrons to higher energy levels, the energy required to keep electrons in lower orbitals is reduced with increased nuclear charge.

Periodic Table Trends

The periodic table is not just a chart of elements but a map demonstrating the periodic trends of atomic properties, including orbital energies. One of the significant trends across periodic periods (the horizontal rows in the periodic table) is the increase in nuclear charge as you move from left to right.
This increased nuclear charge is due to the addition of more protons within the nucleus. As such, the nuclear charge dictates the strength of attraction experienced by outer shell electrons, influencing both the atoms' size and their respective electron configurations. Moreover, because the attractive forces between the nucleus and electrons intensify without a corresponding increase in shielding effect (which is usually contributed by stable inner-shell electrons), orbital energies consequently decline across a period. This trend becomes very noticeable when elements exhibit drastic changes in their chemical placement and properties due to variations in nuclear charge and electron configuration, making this understanding pivotal in predicting the reactivity and bonding behavior of the elements.

Attractive Forces

Attractive forces within an atom play a central role in defining not only the stability of electrons but also their energy levels. These attractive forces originate from the interaction between the positively charged nucleus and negatively charged electrons.
As the nuclear charge of an element increases, say from neon to calcium, the protons in the nucleus exert stronger attractive forces on the electrons. This pull draws electrons closer to the nucleus and further stabilizes them, reducing the overall energy of the orbit they occupy. The effect of these forces is also responsible for the shrinking of atomic radii across the periodic table due to the electrons being held more tightly. In essence, the stronger the attractive force, the lower the energy needed to keep electrons within their orbits, terming the electrons as being in a "lower energy state". Understanding these attractive forces is key to explaining why electrons exhibit specific behaviors, and it helps illustrate the broader framework of periodic trends, particularly how and why orbital energies change.