c97DV2rM / February 17, 2024

Understanding Quantum Numbers and Their Significance in Subatomic Matter

What Are Quantum Numbers?

At the subatomic level, matter behaves in very strange ways. It acts both as a particle and a wave.

Electrons in atoms are found at certain energy levels called orbitals. When an electron transitions to a lower energy level it emits radiant energy in small bundles called photons. This is why Planck’s formula works.

e

e is a mathematical constant that pops up in many different math expressions like logarithms, compound interest and probabilities. It is also the Einstein constant.

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f

A mathematical function that’s used in calculations of logarithms, compound interest, probabilities, and the behavior of quantum particles. It’s also known as the Euler constant.

The p, d and f orbitals have distinctive shapes that reflect their respective levels of energy. The f orbital, for example, looks like a clover with four different possible orientations.

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g

G is the gravitational constant. It is the ratio of the force of gravity to the electron’s mass.

It is used in calculations of logarithms, compound interest, probabilities, the behavior of quantum particles, and more. Like pi, it is a mathematical constant. Its value varies somewhat broadly but remains within an uncertainty limit of about 0.1%. The value of g is very time consuming to calculate with current high-precision measurements.

h

h, also known as Planck’s constant, is a fundamental physical quantity that relates wave-like quantities to particle-like ones. It was first postulated by Max Planck to explain experimental black-body radiation and earned him a Nobel Prize in 1918.

Its value is fixed and used, along with other constants, to define the kilogram, an SI unit of mass. h is important for understanding quantum mechanics.

i

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The first three quantum numbers identify an electron’s principal level, while the fourth number specifies its spin. The Pauli Exclusion Principle states that two electrons can never occupy the same orbital with the same values of these four quantum numbers.

j

The angular momentum quantum number j is the sum of the orbital and spin angular momentum quantum numbers. It is a vector quantity and can only take on values between +j and -j in integer steps.

The j quantum number is encoded with the code letter S in Russell-Saunders term symbols. This allows for a unique state identification in terms of the total energy levels.

k

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The rules limiting allowed combinations of the n and l quantum numbers force electrons to fill out subshells, starting with the most tightly bound state (s). Then they move on into orbitals labelled p, d, f.

l

l is the quantum number that determines the shape of an electron’s wave function. It is also related to the probability that an electron will be in a particular orbital.

It is possible to combine the n and l quantum numbers into a table that shows the allowed orbital shapes for each energy level. This is known as an atomic orbital diagram.

m

The spin quantum number, represented by m, describes how an electron spins. It can have a value of +1/2 or -1/2 and determines the direction an electron goes in an orbital.

The angular quantum number, which describes the shape of an orbital, is represented by l. Purdue University notes that orbitals have spherical shapes when l is 0, polar when l is 1, and cloverleaf-shaped when l is 2.

n

A quantum number that defines the shape of an atomic orbital. It is a key factor in the formation of chemical bonds and spectroscopy.

The principal quantum number, n, defines the different allowed orbits for an electron. An electron at a low energy level has n=1, while an electron at a higher energy level has n=2.

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