Question

Which electron is, on average, closer to the nucleus: an electron in a \(2 s\) orbital or an electron in a \(3 s\) orbital?

Short answer

An electron in a 2s orbital is, on average, closer to the nucleus than an electron in a 3s orbital.

Step-by-step solution

Understanding Electron Orbitals

Electron orbitals describe regions in an atom where electrons are most likely to be found. The number before the 's' (such as 2 or 3) is the principal quantum number, 'n', which indicates the energy level and approximate distance from the nucleus. A higher 'n' value means the electron is in a higher energy level and is, on average, farther from the nucleus.

Comparing the Average Distances

Since the principal quantum number for the 2s orbital is lower than that of the 3s orbital, it can be inferred that electrons in the 2s orbital are, on average, closer to the nucleus than those in the 3s orbital. This is because electrons in orbitals with lower principal quantum numbers are generally closer to the nucleus.

Concluding Which Electron Is Closer

Given that an electron in a 2s orbital has a lower principal quantum number than an electron in a 3s orbital, the electron in the 2s orbital is, on average, closer to the nucleus.

Key concepts

Electron Configuration

Electron configuration is a fundamental key in understanding how atoms interact with each other and form chemical bonds. It describes the arrangement of electrons around the nucleus of an atom. Electrons are organized into layers known as energy levels or shells, and within each level, they are further arranged into subshells known as orbitals. These orbitals are designated as s, p, d, and f, with each type having a different shape.

The 's' orbital, which is spherical in shape, can house a maximum of two electrons, while 'p' orbitals, which are dumbbell-shaped, can hold six electrons and d orbitals can contain ten. The way electrons populate these orbitals is governed by three rules: the Aufbau principle, which dictates that electrons fill the lowest energy orbitals first; the Pauli exclusion principle, stating that no two electrons in an atom can have the same set of four quantum numbers; and Hund's rule, which says that electrons will fill an unoccupied orbital before they pair up.

As a general trend, electrons in lower energy levels and orbitals are closer to the nucleus, making them core electrons that don't typically get involved in bonding. The configuration that tells us where the electrons are likely found is essential for predicting an atom's reactivity and stability in compounds.

Principal Quantum Number

The principal quantum number, designated as 'n', is a crucial part of atomic structure that indicates the energy level an electron occupies in an atom. It's an integer that starts at 1 and increases with increasing energy and distance from the nucleus. The value of 'n' determines the overall size and energy of an orbital, and thus how far an electron is on average from the nucleus.

Each energy level can contain a set number of electrons: the first level with 'n=1' can hold up to 2 electrons, the second level with 'n=2' up to 8 electrons, and so on, increasing according to the formula 2n². Energy and radius generally increase with the principal quantum number, meaning electrons in orbitals with higher 'n' values are less tightly bound to the nucleus and therefore have higher energy levels.

In a scholastic context, understanding the principal quantum number is essential for predicting atomic properties like ionization energy and for explaining periodic trends across different elements in the periodic table.

Atomic Structure

Atomic structure refers to the composition and arrangement of particles within an atom. At the center is the nucleus, containing positively charged protons and neutral neutrons. Electrons, which are negatively charged, whirl around the nucleus in a cloud that represents the probability of finding an electron in a particular location. It's the interplay of these particles that defines the chemical characteristics of an element.

Atomic structure is more than just a simple planetary model of electrons orbiting the nucleus. Quantum mechanics introduces the concept of orbitals, regions in space where there is a high probability of locating an electron. Unlike orbits, which suggest a definite path, orbitals describe a three-dimensional space with differing shapes and orientations.

Understanding the atomic structure includes not only knowing the components of an atom but also appreciating how quantum numbers and electron configurations influence the chemical reactivity and bonding potential of elements. This knowledge is the cornerstone for subjects like chemistry, physics, and materials science.