Question

Write full orbital diagrams and indicate the number of unpaired electrons for each element. (a) \(\mathrm{He}\) (b) \(\mathrm{B}\) (c) \(\mathrm{Li}\) (d) \(\mathrm{N}\)

Short answer

He: 0 unpaired, B: 1 unpaired, Li: 1 unpaired, N: 3 unpaired. Each element's orbital diagram reflects the distribution of electrons with unpaired electrons occupying separate orbitals within a given subshell following Hund's rule.

Step-by-step solution

Write the Electron Configuration

Before drawing the full orbital diagrams, it's necessary to write the electron configurations for each element. For helium (He), with an atomic number of 2, the electron configuration is 1s2. For boron (B), atomic number 5, it is 1s2 2s2 2p1. For lithium (Li), atomic number 3, it is 1s2 2s1. For nitrogen (N), atomic number 7, it is 1s2 2s2 2p3.

Draw Orbital Diagrams for Each Element

The orbital diagrams represent the placement of electrons in each subshell, with boxes or lines indicating the orbitals and arrows indicating the electrons.(a) He: A single box for the 1s orbital with two arrows pointing in opposite directions, representing 2 paired electrons with opposite spins.(b) B: Two boxes for the 1s orbital (both filled with paired electrons), followed by a single box for the 2s orbital (also filled with paired electrons), and then three boxes for the 2p orbitals with only one arrow in one of them signifying a single unpaired electron.(c) Li: Two boxes for the 1s orbital (both filled with paired electrons) and then a single box for the 2s orbital with one arrow, indicating one unpaired electron.(d) N: Two boxes for the 1s orbital (filled with paired electrons), two boxes for the 2s orbital (also with paired electrons), and then three boxes for the 2p orbitals, each with one arrow, indicating three unpaired electrons.

Count the Unpaired Electrons

The unpaired electrons are those not paired up in the same orbital.(a) He: 0 unpaired electrons, as both electrons in helium are paired in the 1s orbital.(b) B: 1 unpaired electron, located in the 2p orbital.(c) Li: 1 unpaired electron, located in the 2s orbital.(d) N: 3 unpaired electrons, located in the 2p orbitals.

Key concepts

Electron Configuration

Understanding electron configuration is crucial for delving into the world of atomic structure and chemistry. It describes how electrons are distributed in an atom's orbitals. Electrons reside in areas around the nucleus called 'orbitals', and each orbital has a maximum number of electrons it can hold. The configuration follows a specific order based on the energy levels called 'Aufbau Principle', filling from the lowest to the highest energy orbital.
For instance, helium (He) has two electrons fitting into the first energy level orbital named '1s'. As a simple rule, the first number represents the energy level, while the 's' shows the type of the orbital, which also determines its shape. Lithium (Li), with three electrons, fills the 1s orbital and places the third electron in the next energy level, the 2s orbital. Boron (B) and nitrogen (N), with five and seven electrons respectively, also fill these lower energy orbitals and then continue to the 2p orbitals.
Learning to write out electron configurations provides the groundwork for creating orbital diagrams, which is a more visual representation of where each electron is located around the atom's nucleus.

Unpaired Electrons

When visualizing electrons in their orbitals, we often encounter the concept of 'unpaired electrons'. These are electrons that are alone in an orbital without a pair. Electrons prefer to pair up because of their opposite spins, which provides stability. However, due to the arrangements of orbitals and the Pauli Exclusion Principle stating that no two electrons in an atom can have the same set of quantum numbers, electrons can end up unpaired.
In our textbook examples, helium (He) has no unpaired electrons, lithium (Li) and boron (B) each have one, and nitrogen (N) has three unpaired electrons. These unpaired electrons are important because they play a significant role in an atom's chemical behavior, especially in bonding and magnetism. Atoms with unpaired electrons are often paramagnetic, which means they are attracted by magnetic fields due to their magnetic moments.

Quantum Mechanics

Quantum mechanics is the branch of physics that deals with the behavior of particles at the atomic and subatomic levels. It gives us a framework for understanding the complex and fascinating behavior of electrons in an atom. Everything we've discussed related to electron configurations and orbital diagrams is governed by quantum mechanics.
In quantum mechanics, electrons are described by wave functions, which provide the probability of an electron's presence in a particular region around the nucleus. This complex concept leads us to the four quantum numbers that specify the 'address' of an electron: principal (energy level), orbital (shape), magnetic (orientation of the orbital), and spin (direction of the electron's intrinsic spin). These principles might be abstract, but they are essential to grasp for an in-depth understanding of how electrons arrange themselves and why they exhibit certain behaviors.

Atomic Structure

Atomic structure refers to the arrangement of the three primary subatomic particles: protons, neutrons, and electrons. The protons and neutrons reside in the nucleus at the center of the atom, with electrons orbiting around in various energy levels and sublevels. The understanding of atomic structure is fundamental in chemistry and physics because it explains the characteristics and behavior of matter.
Orbital diagrams are a fine representation of atomic structure, showing how electrons are arranged in an atom according to specific rules. Through such diagrams, we can see that protons define the element's identity, neutrons add mass but not charge, and electrons account for chemical reactions. Elements differ in atomic structure, so their electron configurations and the number of unpaired electrons vary, influencing their chemical reactivity and bonding patterns.