Question

Suppose the 3s valence electron in a ground-state sodium atom is excited to the 4 s orbital. Why does the electron now have higher energy?

Short answer

In the excitement process, a ground-state sodium atom's 3s valence electron absorbs energy and moves to the 4s orbital, increasing its overall energy. As the electron occupies a higher-energy orbital, it becomes more likely to be found further away from the nucleus, where the electrostatic attraction between the electron and nucleus weakens, resulting in an increase in potential energy. This increased distance and weaker electrostatic force contribute to the electron's higher energy level in the 4s orbital.

Step-by-step solution

Understanding electron orbitals and energy levels

In an atom, electrons occupy different orbitals. They are designated by the quantum numbers: n, l, and m (principal, azimuthal, and magnetic quantum numbers). Each orbital represents a specific energy level for the electron. In ground-state sodium atom, the electron configuration is 1s² 2s² 2p⁶ 3s¹. We are given that a 3s valence electron of a ground-state sodium atom is excited and transferred to the 4s orbital.

Excitation process and energy trade-off

In the excitation process, the electron absorbs a specific amount of energy (usually from light or heat) equal to the energy difference between the two orbitals it's transitioning between (in this case, 3s and 4s). After absorbing the energy, the electron jumps to the higher-energy orbital (4s in our case). Since the electron now occupies a higher energy level within the atom, its overall energy has increased as a result.

Relationship between orbitals and nucleus distance

An electron's likelihood of being located closer or farther away from the nucleus is represented by its orbital. Generally, electrons in higher energy orbitals (larger n) are more likely to be found farther away from the nucleus. In our case, the electron moves from the 3s to 4s orbital, meaning it becomes more likely to be found farther from the nucleus.

Understanding the effect of further distance from the nucleus

As the electron gets further away from the nucleus, the electrostatic attraction between the negatively charged electron and the positively charged protons in the nucleus weakens. This reduction in attractive force allows the electron to have more freedom to move without needing as much energy to escape the nucleus's attraction. Therefore, in the 4s orbital, the electron's potential energy is increased relative to its potential energy in the 3s orbital.

Conclusion

The 3s valence electron in a ground-state sodium atom gets excited and is transferred to the 4s orbital. In this process, the electron absorbs energy, which increases its overall energy. The electron becomes more likely to be found further away from the nucleus in the 4s orbital than in the 3s orbital. As a result, the potential energy and electrostatic force between the electron and nucleus also change, contributing to the increase in the electron's energy in the 4s orbital.

Key concepts

Electron Orbitals

When we talk about electron orbitals, we're referring to the regions within an atom where electrons are most likely to be found. These orbitals are not just simple circles around the nucleus; they come in various shapes and sizes, each characterized by a set of quantum numbers. For example, 's' orbitals are spherical, while 'p' orbitals are shaped like dumbbells.

In the given exercise, a sodium electron is excited from the 3s to the 4s orbital. The number before the 's' indicates the principal quantum number, 'n', which also represents the energy level of the orbital. Larger 'n' values mean the orbital is further from the nucleus, and the electrons within have higher energy. This is why the electron in the 4s orbital has more energy compared to when it was in the 3s orbital.

Quantum Numbers

Each electron in an atom is described by quantum numbers, which dictate its properties and position within the atom. There are four main quantum numbers: the principal (n), azimuthal (l), magnetic (m_l), and spin (m_s) quantum numbers. The principal quantum number determines the energy level of an electron, azimuthal is related to the shape of the orbital, magnetic defines the orientation of the orbital in space, and spin specifies the direction of an electron's spin.

These quantum numbers follow specific rules and are integral to explaining why an electron has higher energy when it moves to an orbital with a higher principal quantum number, such as from 3s to 4s.

Energy Absorption in Atoms

Atoms can absorb energy from external sources, like photons from light or thermal energy. When an atom absorbs the precise amount of energy necessary, one of its electrons can leap from a lower energy orbital to a higher one, a process known as excitation. This leap involves an electron moving from an orbital where it has less freedom to an orbital where it experiences less electrostatic force from the nucleus and hence has more energy.

This phenomenon explains our 3s electron's jump to the 4s orbital in sodium—it absorbs energy equivalent to the gap between these levels. Such energy transitions are fundamental to understanding phenomena such as the emission and absorption spectra of elements.

Electrostatic Attraction in Atoms

Electrostatic attraction is the force that holds electrons in orbit around a nucleus. This attraction occurs because protons in the nucleus are positively charged while electrons are negatively charged, creating a pull between opposite charges. As electrons occupy orbitals further from the nucleus, this attractive force diminishes since the distance between charges directly affects the strength of electrostatic force.

Hence, when an electron transits from the 3s to the 4s orbital, it is moving to a region further from the nucleus where it's held less tightly. This gives the electron more potential energy, as it would now require less energy to remove it from the atom—a concept that's crucial for understanding why the electron's energy is higher in the 4s orbital.