Question

The electron configuration of a neutral atom is \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} .\) Write a complete set of quantum numbers for each of the electrons. Name the element.

Short answer

The quantum numbers for each shell are as follows: \n1s electrons - (1,0,0,±1/2),\n2s electrons - (2,0,0,±1/2),\n2p electrons - (2,1,-1,±1/2), (2,1,0,±1/2), (2,1,1,±1/2) and\n3s electrons - (3,0,0,±1/2).\nThe element is Magnesium.

Step-by-step solution

Electron Configuration Interpretation

The electron configuration '1s² 2s² 2p⁶ 3s²' tells us about the distribution of electrons in the atomic shells and subshells. It means there are two electrons in the '1s' subshell, two electrons in the '2s' subshell, six electrons in the '2p' subshell, and two electrons in the '3s' subshell.

Quantum Numbers for 1s Electrons

For the two electrons in the '1s' subshell: \[n = 1, l = 0, m = 0\]. The spin quantum numbers will differentiate the two electrons, so one will have spin (+1/2), the other (-1/2).

Quantum Numbers for 2s Electrons

For the two electrons in the '2s' subshell: \[n = 2, l = 0, m = 0\]. Again, the two electrons will differ by their spin quantum numbers (one with +1/2, the other with -1/2).

Quantum Numbers for 2p Electrons

For the six electrons in the '2p' subshell: \[n = 2, l = 1, m = -1, 0, 1\]. With three different magnetic quantum numbers, each could accommodate two electrons, one with a +1/2 spin and the other with a -1/2 spin.

Quantum Numbers for 3s Electrons

For the two electrons in the '3s' subshell: \[n = 3, l = 0, m = 0\]. Once more, the two electrons differ by their spin quantum numbers.

Determining the Element

The total number of electrons can be found by adding up all the electrons in the configuration: 2+2+6+2 = 12. A neutral atom with 12 electrons is the element magnesium, as atomic number equals the number of electrons in a neutral atom.

Key concepts

Quantum Numbers

Quantum numbers are essential for describing the properties of electrons within an atom. They provide a unique address for each electron, allowing us to understand its position and energy level very precisely. There are four quantum numbers:

• Principal Quantum Number ( n ): This indicates the main energy level or shell of an electron. For instance, for the 1s, 2s, and 3s subshells, n corresponds to 1, 2, and 3 respectively.


• Angular Momentum Quantum Number ( l ): This specifies the subshell and the shape of the orbital. It determines the shape of the path that the electron takes around the nucleus. For s, p, d, and f subshells l is 0, 1, 2, and 3 respectively.


• Magnetic Quantum Number ( m ): This provides information about the orientation of the orbital in space. For example, the 2p subshell has three orientations, so m can be -1, 0, or +1.


• Spin Quantum Number: This details the direction of the electron's spin, either +1/2 or -1/2, ensuring two electrons can share the same orbital within one subshell.

Every electron in an atom has its own set of these quantum numbers, ensuring that no two electrons share the same address. This is known as the Pauli Exclusion Principle.

Atomic Structure

The atomic structure defines the organization of electrons, protons, and neutrons within an atom. At its core, an atom consists of:

• Nucleus: This contains protons, which are positively charged, and neutrons, which have no charge. Together, they form the heavy central part of the atom.


• Electron Cloud: Electrons, which are negatively charged, orbit around the nucleus in regions called orbitals. These orbitals are grouped into energy levels or shells.

An atom's identity is predominantly determined by the number of protons in its nucleus, known as the atomic number. Protons and neutrons have significant mass compared to electrons, which are much lighter and occupy most of the space of an atom.
To accommodate their charges and energies, electrons occupy distinct subshells within these shells (e.g., 1s, 2p), described by our earlier discussion on quantum numbers. Understanding atomic structure helps us explain how atoms interact in chemical reactions and how they form molecules.

Magnesium

Magnesium is the element represented by the atomic number 12, meaning it has 12 protons in its nucleus and, when neutral, 12 electrons. Its electron configuration is 1s^2 2s^2 2p^6 3s^2 , which shows the distribution of electrons across different subshells and energy levels.
In the periodic table, magnesium is situated in group 2, the alkaline earth metals, characterized by two electrons in their outermost s subshell. This configuration makes magnesium fairly reactive, usually losing its two outer electrons to achieve a stable electron structure similar to the noble gas neon.

• Reactivity: Magnesium often forms compounds by reacting with oxygen, chlorine, and other nonmetals. Its reactivity is moderate compared to alkali metals in group 1.


• Physical Properties: Magnesium is lightweight, silvery-white, and strong, making it ideal for applications requiring low density and high strength-to-weight ratio, like in aerospace engineering.

Understanding magnesium's position in the periodic table and electron configuration helps predict and rationalize its chemical behavior and applications.