Question

The elements \(\mathrm{Si}, \mathrm{Ga}\), As, \(\mathrm{Ge}, \mathrm{Al}, \mathrm{Cd}, \mathrm{S}\), and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configuration for these atoms.

Short answer

The electron configurations for the given elements are: \(Si: 1s^2 2s^2 2p^6 3s^2 3p^2 \\ Ga: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^1 \\ As: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3 \\ Ge: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2 \\ Al: 1s^2 2s^2 2p^6 3s^2 3p^1 \\ Cd: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} \\ S: 1s^2 2s^2 2p^6 3s^2 3p^4 \\ Se: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^4 \)

Step-by-step solution

Identifying the Atomic Number

First, find the atomic number (number of protons) of each element using the periodic table. The atomic number will also tell us how many electrons are present in a neutral atom. \(Si: Z = 14 \\ Ga: Z = 31 \\ As: Z = 33 \\ Ge: Z = 32 \\ Al: Z = 13 \\ Cd: Z = 48 \\ S: Z = 16 \\ Se: Z = 34 \)

Finding the Electron Configuration

Next, starting with the lowest energy orbital, we fill in the electrons following the Aufbau principle, Pauli exclusion principle, and Hund's rule. Here are the electron configurations for each element: \(Si: 1s^2 2s^2 2p^6 3s^2 3p^2 \\ Ga: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^1 \\ As: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3 \\ Ge: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2 \\ Al: 1s^2 2s^2 2p^6 3s^2 3p^1 \\ Cd: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} \\ S: 1s^2 2s^2 2p^6 3s^2 3p^4 \\ Se: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^4 \) So, the electron configurations for each of the given elements are: \(Si: 1s^2 2s^2 2p^6 3s^2 3p^2 \\ Ga: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^1 \\ As: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3 \\ Ge: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2 \\ Al: 1s^2 2s^2 2p^6 3s^2 3p^1 \\ Cd: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10} \\ S: 1s^2 2s^2 2p^6 3s^2 3p^4 \\ Se: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^4 \)

Key concepts

Semiconductor Elements

Semiconductor elements play a crucial role in modern electronics. They are used in the production of semiconductor devices like diodes and transistors. Generally, semiconductor elements are found in group 14 and neighboring groups of the periodic table, including elements like Silicon (Si), Germanium (Ge), and Gallium (Ga). Silicon is the most widely used due to its abundance and favorable electronic properties.
Semiconductors are materials that have an electrical conductivity between that of an insulator and a conductor. This unique property arises because of the energy band structure and the electron configuration. In semiconductors, the electron configuration defines how electrons are organized in atoms. They can move more freely compared to insulators, allowing these materials to conduct electricity under certain conditions.
Understanding the electron configuration of semiconductor elements is key to designing electronic devices that are efficient and effective. This involves studying how these elements' electrons are distributed across different energy levels, enabling them to interact favorably with electric fields.

Aufbau Principle

The Aufbau principle is a fundamental concept in chemistry that guides the filling of electron orbitals in atoms. The term 'Aufbau' is German for 'building up', representing how electrons occupy orbitals starting from the lowest energy level upward. This is crucial in determining the electron configuration for elements. For example, in the case of Silicon (\(Z = 14\)), the electron configuration proceeds as \(1s^2 2s^2 2p^6 3s^2 3p^2\).

• Electrons fill orbitals in order of increasing energy levels, which generally follow this order: \(1s, 2s, 2p, 3s, 3p,...\).
• The 'building up' order can be remembered using the energy level diagram or using the diagonal rule.

This principle helps to systematically determine the electron arrangement, which is crucial in predicting chemical properties and behavior of elements, especially those used in semiconductors.

Pauli Exclusion Principle

The Pauli exclusion principle, formulated by Wolfgang Pauli, states that no two electrons in an atom can have the same set of four quantum numbers. This principle helps define the electron configuration within an atom. Here, each electron in an atom is unique in terms of its quantum state.

• The principle ensures that each orbital can hold a maximum of two electrons, each with opposite spins (one spin-up \((+\frac{1}{2})\) and one spin-down \((-\frac{1}{2})\)).
• This rule is essential in maintaining the structure and stability of an atom. It prevents electrons from 'piling up' in the lowest energy states.

In semiconductor elements, the Pauli exclusion principle dictates how electrons occupy energy levels, influencing their electrical and thermal conductivity. It plays a vital role in the behavior of semiconductor devices.

Hund's Rule

Hund's rule is a principle explaining how electrons are distributed among orbitals of the same energy level. It states that every orbital in a sublevel is singly occupied before any orbital is doubly occupied and all electrons in singly occupied orbitals have the same spin direction.

• This rule maximizes the number of unpaired electrons, which in turn influences the magnetic and chemical properties of an element.
• For example, in the \(3p\) sublevel of Sulfur (\(S\)), having the configuration \(3s^2 3p^4\), Hund's rule dictates that electrons will occupy three \(3p\) orbitals as singly as possible before pairing occurs.

By understanding Hund's rule, one gains insight into how electron configurations can be manipulated to enhance the conductive properties in semiconductor elements, crucial for the development of both traditional and new technologies.