What is the electronic configuration of the ground state of...

What is the electronic configuration of the ground state of the carbon atom? Write it in the following ways: (a) using spectroscopic notation $\left(1 s^{2}, \ldots\right) ;$ (b) listing the four quantum numbers for each of the electrons. Note that there may be more than one possibility in (b).

What is the electronic configuration of the ground state of the carbon atom? Write it in the following ways:
(a) using spectroscopic notation $\left(1 s^{2}, \ldots\right) ;$ (b) listing the four quantum numbers for each of the electrons. Note that there may be more than one possibility in (b).

Key Concepts

Quantum Numbers

Quantum numbers are four values that uniquely characterize each electron in an atom. These include the principal quantum number (n), the azimuthal or orbital angular momentum quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s). They specify details such as the electron's energy, shape, orientation, and spin, and are fundamental to understanding atomic structure.

Ground State

The ground state of an atom refers to its lowest energy configuration. In this state, the electrons are arranged in the most stable way possible, occupying the lowest energy orbitals available. This concept is important because the physical and chemical properties of an atom are largely determined by its electrons in the ground state.

Electronic Configuration

This concept describes the distribution of electrons among the various atomic orbitals in an atom. It is arranged in order of increasing energy and follows established rules such as the Pauli exclusion principle and Hund's rule, which dictate that no two electrons can have the same set of quantum numbers and that electrons will occupy degenerate orbitals singly before pairing up.

Spectroscopic Notation

Spectroscopic notation is a compact way to represent an atom's electronic configuration by listing orbitals (using numbers for the principal quantum number and letters for the orbital type) along with superscripts indicating the number of electrons in each orbital. This notation simplifies the visualization and communication of electron distributions in atoms.

Transcript

00:01 In this exercise, we have to find the ground state electronic configuration of the carbon that has an atomic number of 6.

00:06 And in question a, we have to write it in the spectroscopic notation.

00:13 Here, on the left, i have drawn the order according to which we should allocate atoms to, i'm sorry, allocate electrons to subshells in atoms.

00:27 So let's do it for the carbon.

00:28 First, we put two electrons in the 1s subshell, then two in the 2s subchel.

00:36 Notice that there are four electrons already placed, so we have only two to go.

00:44 The next sub -shell is the 3, i'm sorry, is the 2p, and 6 electrons can fit in the 2p sub -shell, but we only need 2.

01:00 So this here is the electronic configuration of the carbon.

01:06 In question b, we have to write the electronic configuration by explicitly writing the four quantum numbers.

01:16 Okay, so the four quantum numbers are n, l, so the principal quantum number is n, the orbital quantum number is l, the magnetic quantum number is ml, and the spin quantum number is ms.

01:33 So we have these four quantum numbers.

01:41 Okay.

01:42 And for the electron, the two electrons in the 1s shell, n is one, that's the principal quantum number, l can only be zero, okay, because the s shell has an angular, angular momentum of zero.

02:00 Ml can also only be zero because ml can range from minus l to l, but l...

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