Consider these sets of four quantum numbers for electrons in...

Consider these sets of four quantum numbers for electrons in an atom. $$ \begin{array}{l} \text { (i) } n=2, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2} \\ \text { (ii) } n=2, \ell=0, m_{\ell}=1, m_{s}=0 \\ \text { (iii) } n=2, \ell=1, m_{\ell}=1, m_{s}=-\frac{1}{2} \\ \text { (iv) } n=2, \ell=0, m_{\ell}=1, m_{s}=-\frac{1}{2} \end{array} $$ (a) Identify the two electrons that have the same spin. (b) Identify the two electrons that are in the same atomic orbital.

Consider these sets of four quantum numbers for electrons in an atom.
$$
\begin{array}{l}
\text { (i) } n=2, \ell=1, m_{\ell}=1, m_{s}=+\frac{1}{2} \\
\text { (ii) } n=2, \ell=0, m_{\ell}=1, m_{s}=0 \\
\text { (iii) } n=2, \ell=1, m_{\ell}=1, m_{s}=-\frac{1}{2} \\
\text { (iv) } n=2, \ell=0, m_{\ell}=1, m_{s}=-\frac{1}{2}
\end{array}
$$
(a) Identify the two electrons that have the same spin.
(b) Identify the two electrons that are in the same atomic orbital.

Key Concepts

Atomic Orbitals

Atomic orbitals are regions around an atom's nucleus where electrons are most likely to be found. These orbitals are defined by a specific combination of quantum numbers (n, ?, and m?). Electrons that share the same orbital have identical values for these three quantum numbers, though they may differ in their spin (m?) to comply with electron configuration rules.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a quantum mechanical rule stating that no two electrons in an atom can have the same set of all four quantum numbers. This principle forces paired electrons within the same orbital to have opposite spins and governs the electron configuration in atoms, thereby influencing the chemical properties and behavior of elements.

Quantum Numbers

Quantum numbers are a set of values that describe the unique state of an electron in an atom. They include the principal quantum number (n), which indicates the energy level; the angular momentum quantum number (?), which defines the subshell shape; the magnetic quantum number (m?), which specifies the orbital’s orientation; and the spin quantum number (m?), which represents the electron's intrinsic spin direction. Together, these numbers distinguish one electron from another within atoms.

Electron Spin

Electron spin is a fundamental property of electrons, representing their intrinsic angular momentum. Expressed as either +½ or -½, this quantum number indicates the direction of the electron's spin. The value of m? plays a crucial role in determining how electrons fill orbitals and abide by the exclusion principle, ensuring that even electrons occupying the same orbital must have opposite spins.

Transcript

00:01 The given question is on the topic electronic configuration and the predictable.

00:05 In this question it is asked that consider these set of four quantum numbers for electrons in an atom.

00:10 So, there are four set of data given and we have been asked to find the answer for the following questions.

00:15 The first one is identify the two electrons that have the same spin and identify the two electrons that are in the same atomic orbitals.

00:21 Now from the concept that we know about quantum numbers, we know that the out of n is the significance of shell and is also called as principal quantum number and it signifies shell or shell number of an atomic orbital.

00:49 L is called as asymmethyl quantum number, it is called as amethyl quantum number and it signifies the sub shell.

01:04 It signifies the sub shell.

01:07 Ml signifies magnetic quantum number, magnetic quantum number and how about and it's the significance of orbital it signifies which orbital the electron is in and the last one ms are also called as the spin quantum number gives an idea about what is the spin that electron is having right now.

01:35 So, ms is the significance of the spin that an electron has.

01:41 So now let's look at the question, spin quantum number, which gives an idea about the spin of electron.

01:57 So let's have an idea and look at the question to solve this.

02:01 So first one, part a of the question says, and we have two electrons that have the same spin.

02:08 So spin is determined by ms...

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