Azimuthal Quantum Number – Quantum Numbers, History, Types, Importance, Practice Problems and FAQ

Let's say you are travelling from New Delhi to Visakhapatnam by train. You see that there is a 40-minute stop at Bhopal junction when you look at the train itinerary. Fortunately, you have an old buddy who lives in Bhopal who you haven't seen in a long time. You call him on the phone and invite him to come to see you at the train station.

How will your friend find you at the railway station?

You might believe that since you are acquainted, he won't have a hard time locating you. However, a railway station has 4-5 platforms and an average train has 24 carriages. Without knowing your train, coach, and seat number, he won't be able to locate you. So that your friend can quickly locate you, you provide a snapshot of your train ticket to avoid this issue.

Your ticket contains information such as the train number, departure time, coach number, and seat number. It also informs you of the likely location where finding you will be maximum.

Similarly, electrons can also be found in probable locations and these probable locations are denoted using quantum numbers.

On this concept page, we will get to know more about azimuthal quantum numbers in detail.

TABLE OF CONTENTS

Quantum Numbers – Introduction
Quantum Numbers – Types
Principal Quantum Number
Magnetic Quantum Number
Electron Spin Quantum Number
Azimuthal Quantum Number
Quantum Numbers – Need
Quantum Numbers – Importance
Practice Problems
Frequently Asked Questions – FAQ

Quantum Number – Introduction

An atom contains many orbitals. Thes orbitals are defined by a set of numbers called quantum numbers. To specify the shape, size and energy of the orbitals, three quantum numbers namely the principle quantum number (n), azimuthal quantum number (l) and magnetic quantum number (ml) are required. To specify the electron, an additional quantum number called spin quantum number (ms) is required. Thus each orbital in an atom is assigned three quantum numbers and each electron in an atom is assigned four quantum numbers.

Quantum Numbers – Types

1. Principal Quantum Number (n)
2. Azimuthal Quantum Number (l)
3. Magnetic Quantum Number (ml)
4. Spin electron Quantum Number (ms)

Principal Quantum Number

Principal quantum number determines the size and the energy of an orbital and is denoted by 'n'. Higher the value of n indicates a bigger size of the orbital.

Size of orbital ∝ n

Energy of the orbital ∝ n

Principal quantum number has always a positive integer value ( n = 1, 2, 3, …) and it helps us to identify the shell.

n	1	2	3	4
Shell	K	L	M	N

Magnetic Quantum Number

Magnetic quantum number determines the number of preferred orientations of the orbitals in a subshell. It is donated by ‘mℓ’. The mℓ can have (2l+1) values ranging from -l to +l (all the integer values including 0). Magnetic quantum number describes the behaviour of electrons in a magnetic field.

Electron Spin Quantum Number

The electron spin quantum number is independent of the values of n, l, and mℓ. The value of this quantum number, which denotes the direction in which the electron is spinning, is represented by the symbol "ms". The direction of the electron's spin can be determined by looking at the value of ms. There are two possible values for the electron spin quantum number: 12 and -12.

Azimuthal Quantum Number

Azimuthal quantum number is also referred to as subsidiary quantum number or orbital angular momentum quantum number. It is generally denoted by 'l'.

It defines the three-dimensional shape of the orbital.

It designates the subshell to which the electron belongs.

Its value is equal to the total number of angular nodes in the orbital.

For a given value of principal quantum number (n), ‘l’ can have values ranging from 0 to n – 1.

The azimuthal quantum number, for instance, can be 0, 1, or 2 if n = 3.

When l=0, the resulting subshell is a "s" subshell.

Value for l	Subshell	Description	Shape
0	s	Sharp	Spherical
1	p	Principal	Dumbbell
2	d	Diffuse	Double-dumbbell
3	f	Fundamental	Complex

The resulting subshells are 'p' and 'd' subshells, respectively, when l=1 and l=2 (respectively). The three subshells that can be used when n equals three are 3s, 3p, and 3d.

In a different illustration, when the value of n is 5, the possible values of l are 0, 1, 2, 3, and 4. If l = 3, the atom has three angular nodes.

Orbital angular momentum

ħ=h2

Where l=azimuthal quantum number

Value for n	1	2	3	4
Value for l	0	0,1	0,1,2	0,1,2,3
Notation for subshell	1s	2s,2p	3s,3p,3d	4s,4p,4d & 4f
Number of subshell	1	2	3	4
Orbital angular momentum = l(l+1) h2	0	h2	6h2	3h2

Quantum Numbers – Need

We use a series of specific integers known as quantum numbers to describe the location of an electron in an associated atom. Quantum numbers can be used to describe the characteristics of atomic orbitals and the electrons within them.

The configuration of an electron in an atom or ion is described by a set of four quantum numbers. Take into account that they are important variables in an equation that describes the three-dimensional location of electrons in a specific atom. Before pairing up, electrons first occupy the orbitals by themselves.

A maximum of two electrons can fit in each orbital, and they will be oriented in opposition to one another. The other electron will spin down if one is spinning up.

It also indicates whether or not the atom is capable of creating magnetic fields. An electron behaves like a small magnet because of spin.

If all of the electrons in an atom are paired together in their orbitals, their spins cancel each other out and the atom is said to be diamagnetic. They repel magnetic fields when we add up all of their spins because the total is zero. This is the case with the electronic configuration of Mg in its ground state (all of its electrons are paired, making it diamagnetic).

The orbital diagram of Mg:

When an atom has unpaired electrons in its orbitals, those electrons have a net spin and the spins do not cancel out. The atom now has a net spin and is drawn to a magnetic field as a result. Such atoms are called paramagnetic species. The electronic configuration of O- It has 1 unpaired electron, so it's paramagnetic.

The orbital diagram of O-:

Aspects of electrons include their configuration, spin, and location within an atom. Quantum numbers characterise these qualities.

Quantum Numbers – Importance

Help in determining the electronic configuration of an atom.

Describe where electrons are most likely to be.

Aid in comprehending atomic characteristics like ionisation energy and atomic radius.

Practice problems

In an orbital, when two electrons are present, which quantum number can differentiate between the two electrons?

Principal quantum number
Azimuthal quantum number
Spin quantum number
Magnetic quantum number

Answer: C

Solution: The two electrons occupying the same orbital can never have the same spin. The spin quantum number can be either +12 or-12 and distinguishes the two electrons present in the same orbital.

So, option C is the correct answer.

When n = 3, l = 1, mℓ = 0, the number of orbitals is:

Answer: D

Solution: Since n=3 (principal quantum number) and l=1 (azimuthal quantum number), it is a 3p-orbital, and since mℓ=0 (the magnetic quantum number) the given 3p-orbital is 3pz. As a result, the given quantum numbers can only identify a maximum of one orbital i.e. 3pz.

So, option D is the correct answer.

n = 3, l = 1, mℓ = -1. Predict the maximum number of electrons that can have the given quantum numbers?

Answer: C

Solution: n=3,l=1 and mℓ=1 implies that it is an orbital of the 3p subshell. Any orbital can have a maximum of 2 electrons with spin quantum number ± 12. Therefore, the maximum number of electrons with n=3,l=1,mℓ=1 is 2.

So, option C is the correct answer.

When an orbital has the quantum numbers n=3 and l=1, how many electrons can be present?

Answer: A

Solution: n=3 and l=1 implies that it is an orbital of 3p subshell. 3p shubshell contains 3 orbitals and each orbital can have 2 electrons. Therefore the quantum numbers n=3 and l=1 can hold a maximum of six electrons.

So, option A is the correct answer.

Frequently Asked Questions – FAQ

1. The principal quantum number can not have which value?
Answer: The value of the principal quantum number (n) can never be zero. The permitted values for n are 1, 2, 3, 4, and so forth.

2. Which quantum number determines the shape of an orbital?
Answer: The integer value of the angular momentum quantum number, l, can range from 0 to n - 1. The type or shape of the orbital is indicated by this quantum number.

3. What is the source of quantum numbers?
Answer: Atomic orbitals are precisely distinguished by quantum numbers. These quantum numbers are obtained from the solution of the Schrodinger wave equation.

4. What are degenerate orbitals?
Answer: Orbitals having the same energy are called degenerate orbitals. Lower energy levels are filled before higher energy levels, according to the Aufbau principle.

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