Question

What is the maximum number of electrons that can go into the first shell? The second shell? The third shell?

Short answer

First shell: 2 electrons, Second shell: 8 electrons, Third shell: 18 electrons.

Step-by-step solution

Understand the Electron Shell Concept

Electrons in an atom are arranged in shells or energy levels around the nucleus. Each shell can hold a maximum number of electrons, determined by the formula \(2n^2\), where \(n\) is the shell number.

Calculate Maximum Electrons for the First Shell

For the first shell, \(n = 1\). Apply the formula: \(2n^2 = 2(1)^2 = 2\). Therefore, the first shell can hold a maximum of 2 electrons.

Calculate Maximum Electrons for the Second Shell

For the second shell, \(n = 2\). Use the formula: \(2n^2 = 2(2)^2 = 8\). So, the second shell can hold a maximum of 8 electrons.

Calculate Maximum Electrons for the Third Shell

For the third shell, \(n = 3\). Apply the formula: \(2n^2 = 2(3)^2 = 18\). Thus, the third shell can hold a maximum of 18 electrons.

Key concepts

electron shells

Electron shells are regions around the nucleus of an atom where electrons are likely to be found. Each shell represents a specific energy level, and electrons occupy these shells in a way that minimizes the energy of the atom. This arrangement follows a simple principle of providing electrons the least energy-demanding space first.

• The first electron shell is closest to the nucleus and thus has the lowest energy and is filled first.
• Subsequent shells are higher in energy but can hold more electrons.
• The capacity of each shell can be determined by the formula \(2n^2\), where \(n\) is the shell number.

For example, the first shell can hold up to 2 electrons, the second shell can hold up to 8 electrons, and the third shell can accommodate up to 18 electrons. This distribution is essential for understanding how atoms bond and interact with each other in chemical reactions.

atomic structure

Atoms are the basic building blocks of matter and comprise protons, neutrons, and electrons. The protons and neutrons reside in the nucleus at the center of the atom and carry the majority of the atom’s mass. Electrons, which are much lighter, orbit this nucleus in electron shells.

• Protons have a positive charge, while electrons have a negative charge, causing an electrostatic attraction that keeps the electrons in motion around the nucleus.
• Neutrons have no charge and add to the mass of the nucleus.
• The number of protons in the nucleus defines the atomic number and, consequently, the element.

The arrangement of electrons in shells around the nucleus influences the chemical properties of an element and is known as its electron configuration. Changes in this arrangement are what drive chemical reactions and the formation of molecules.

quantum numbers

Quantum numbers are a set of values that describe the specific state of an electron in an atom. These numbers explain the unique position and energy of electrons in the atomic structure, ensuring no two electrons in an atom have the same set of quantum numbers, following Pauli's exclusion principle.

• The principal quantum number \(n\) indicates the main energy shell of an electron and can have positive integer values like 1, 2, 3, etc.
• The azimuthal quantum number \(l\) defines the shape of the orbital, with values ranging from 0 to \(n-1\).
• The magnetic quantum number \(m_l\) shows the orientation of the orbital within a shell and can range from \(-l\) to \(+l\).
• The spin quantum number \(m_s\) describes the spin orientation of the electron, with possible values of +1/2 or -1/2.

Understanding these numbers helps in visualizing the three-dimensional space where electrons are probable to exist, which is crucial in predicting how atoms will interact in a chemical setting.