Question

The electron in the same orbital may be identified with the quantum number (a) \(n\) (b) \(l\) (c) \(m\) (d) s

Short answer

The electron in the same orbital may be identified with the quantum number (d) s.

Step-by-step solution

Understanding Quantum Numbers

There are four quantum numbers used to describe the unique state of an electron in an atom: the principal quantum number (), the azimuthal or angular momentum quantum number (), the magnetic quantum number (), and the spin quantum number ().

Identifying the Correct Quantum Number

The quantum number determines the energy level and size of the orbital. The quantum number defines the shape of the orbital. The quantum number specifies the orientation of the orbital in space. The quantum number describes the spin of the electron and can have only two possible values (+1/2 or -1/2), allowing electrons in the same orbital to be differentiated from one another.

Choosing the Correct Answer

Since we are looking to identify electrons in the same orbital, the spin quantum number (s) is used because it differentiates electrons with the same n, l, and m values within the same orbital by their spin orientation.

Key concepts

Electron Configuration

When understanding the complex world of atoms, it's essential to start with the 'electron configuration', which refers to the distribution of electrons among the various atomic orbitals. It's akin to how residents are arranged within an apartment complex; each electron has its 'apartment' (orbital) within an 'apartment building' (energy level).

The 'principal quantum number' () acts as the address for the energy level or 'floor' where the electron resides. Higher values denote further and higher energy levels from the nucleus. As we move to higher floors in a building, we get a broader view. Similarly, electrons in higher energy levels have more potential energy.

Ruling the Block: Subshells and Orbitals

Within each energy level are sub-levels or 'subshells' marked by the 'azimuthal quantum number' (), resembling different sections of each floor in our building analogy. These subshells define the shape of electron neighborhoods — whether they are spherically shaped (=0), dumbbell-shaped (=1), and so on, which leads to a diverse range of possible configurations.

• =0: s subshell (1 orbital)
• =1: p subshell (3 orbitals)
• =2: d subshell (5 orbitals)
• =3: f subshell (7 orbitals)

Just like each apartment can have a specific orientation or view — cityscape, seaside, etc., the 'magnetic quantum number' () defines the orientation of an orbital within a subshell. It can vary from - to +.

Electrons fill these 'apartments' following the 'Aufbau principle', which instructs that lower energy 'apartments' must be occupied before the higher ones. This hierarchical structure helps predict the electron arrangement and plays a critical role in understanding the chemical properties of elements.

Atomic Orbitals

Atomic orbitals are the heart of any discussion about electron behaviors and positions. Just like homes come in different architectural designs, 'atomic orbitals' vary in shape, encompassing the regions in space where there is a high probability of finding an electron.

The azimuthal or angular momentum quantum number () reveals the shape of these orbitals. For instance:

• =0 gives us the spherically symmetric s-orbitals.
• =1 gives rise to the dumbbell-shaped p-orbitals.
• Higher values lead to more complex d and f orbitals.

Imagine these shapes as different seating arrangements in a theater; some face the stage (nucleus) directly, while others offer a side or oblique view.

Each orbital is a home to a maximum of two electrons. Just as two people sharing a room distinguish their personal space, electrons within the same orbital are differentiated by their 'spin quantum number'.

Picturing the Invisible

To grasp atomic orbitals further, we must sometimes rely on probability distributions or electron density maps. These visual aids are much like heatmaps that show us where we're most likely to encounter electrons, providing a graphical representation of their potential whereabouts. It's important to note that while these models give us insight, they can't pinpoint exact locations due to the intrinsic nature of quantum mechanics.

Spin Quantum Number

In the realm of the extraordinarily tiny, the 'spin quantum number' () imparts a unique characteristic to every electron, akin to fingerprints for humans. It represents an intrinsic form of angular momentum, not directly analogous to everyday spinning objects but nevertheless a critical aspect of an electron's identity.

This quantum number can assume one of only two possible values: +1/2 or -1/2, often denoted as 'spin-up' or 'spin-down'. It's the final piece needed to fully distinguish one electron from another in the same apartment (orbital). Just like two people might share an address but have different names, two electrons in the same orbital have the same , , and values, but must differ in their values.

A Delicate Balance

The Pauli Exclusion Principle comes into play here, stating that no two electrons in an atom can have the exact same set of all four quantum numbers. This ensures each electron is unique and enables the balance and diversity of electron arrangements across different elements. Now, when electrons with opposite spins are paired in an orbital, the energy of the atom becomes more stable — a kind of 'roommate compatibility' that affects their living arrangement's harmony!