Give the maximum number of electrons in an atom that can have these quantum numbers: a. n=0, ℓ=0

Give the maximum number of electrons in an atom that can...

Key Concepts

Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of four quantum numbers. This principle is fundamental in determining the arrangement of electrons in orbitals, ensuring that even if electrons share the same spatial orbital (same n, ?, and m?), they must differ in their spin quantum number.

Orbital Capacity and Electron Configuration

Orbital capacity refers to the number of electrons that can occupy a particular orbital or set of quantum numbers. Typically, each orbital defined by a unique combination of n, ?, and m? can accommodate up to two electrons (one for each spin state). This concept plays a crucial role in constructing electron configurations and understanding the structure and periodicity of the elements.

Spin Quantum Number (m?)

The spin quantum number, m?, describes the intrinsic spin of an electron, which is a fundamental property independent of its orbital motion. Its allowed values are +1/2 or -1/2, meaning that each orbital can hold a maximum of two electrons with opposite spins.

Magnetic Quantum Number (m?)

The magnetic quantum number, m?, specifies the orientation of the orbital in space. Its allowed values range from -? to +?, including zero. This quantum number is important for understanding the spatial distribution of electrons and how orbitals are arranged in an external magnetic field.

Angular Momentum Quantum Number (?)

The angular momentum quantum number, represented as ?, determines the shape of the electron’s orbital. It takes on integer values ranging from 0 to n-1 for a given principal quantum number, and each value of ? corresponds to a specific type of orbital (s, p, d, f, etc.).

Principal Quantum Number (n)

The principal quantum number, denoted as n, indicates the energy level or shell in which an electron is found. It primarily determines the electron’s distance from the nucleus and the overall size of the orbital. Higher values of n correspond to electrons that are further from the nucleus and typically higher in energy.

Quantum Numbers

Quantum numbers are a set of numerical values that describe the properties and state of an electron in an atom. They include the principal quantum number, angular momentum quantum number, magnetic quantum number, and spin quantum number. Each number provides specific information about the electron’s energy, shape, orientation, and intrinsic spin, and together they uniquely define the electron's state in an atom.

Transcript

00:01 Guys doing problem? 80 of chips seven give the maximum number of electrons and adam that have these quantum numbers and equal zero l equals zero ml eagles here.

00:11 So when and equals year girl, uh, and cannot equals here and is a 1234 so this this whole thing is incorrect act also n and l cannot be equivalent each other.

00:33 So that's not a correct operations.

00:36 Oh, the number zero.

00:38 So 2nd 1 and equals two and help equals one.

00:44 And so when an eagles to that second energy level illegals one that correspond to a p orbital and ml is equal negative one.

00:54 So when we do our orbital's let's say we have a pure girl down here and these air ml vase.

00:59 So remember what ml ml is the range between l buy.

01:03 So in this case, it's the grand prix negative one m and positively betweennegative l and possible so negative because we put one number two refugees, one negative, 10 and one, so there can only be so this could only correspond to one orville.

01:22 And the maximum number of electrons that can be in there is too so and equals three and m s is equal to 1/2 so so whenever you have an electron in orbital, you can have one that spin up, which no positive 1/2 spin on one that's been doubt just got negative 1/2 spin.

01:44 So let's say if this entire entire ordeal philip, we would fill up with six electrons, and the number that we spent up will be three number that be spent down b would be three.

01:56 So it's just have been a the ones they're gonna have this configuration, or half the electrons in the and equals three energy level.

02:04 So the ones that have an equals three energy level those are three s with just two electrons creepy, which has six electrons and three d, which has 10 electrons...

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