Question

Explain Magnetic Quantum number.

Answer 1

Quantum number: The set of numbers which is used to determine the position, energy and spin of an electron in an atom is known as Quantum numbers. These are categorized into four types, Principal Quantum number, Azimuthal Quantum number, Magnetic Quantum number and spin quantum number.

Complete answer:
Magnetic Quantum number:
It determines the total number of orbitals in any subshell and orientation of the orbitals in space. It gives the projection of angular momentum related to the orbital along a fixed axis. It is symbolized as ${m_l}$.
The values of magnetic quantum numbers depend on the values of azimuthal quantum number which is denoted by the symbol $l$. The values of magnetic quantum numbers lie between the range $- l$ to $+ l$. As the value of $l$ depends on the value of $n$ i.e., principal quantum number, so magnetic quantum number also depends on the value of $n$ indirectly.
For example: Let’s find out the value of the magnetic quantum number for the last electron of a nitrogen atom.
Atomic number of nitrogen atom $= 7$
Electronic configuration of nitrogen atom $= 1{s^2}2{s^2}2{p^3}$
As the last electron is present in the second shell. So, the value of the principal quantum number $n = 2$.
The value of azimuthal quantum number $l = 0$to $n - 1$. So, for given conditions values will be $0,1$.
Because the last electron is present in $p -$orbital. Therefore, the value of $l$ corresponds to $p -$orbital is $1$.
The range of values for ${m_l}$ is $- l$ to $+ l$ i.e., $- 1,\,0,\, + 1$.
Hence the value of magnetic quantum number for the last electron of nitrogen atom is $+ 1$

Note:
The total number of orbitals in any shell is a function of azimuthal quantum number which is related by the formula $2l + 1$. The number of orbitals present represent the total number of possible values of magnetic quantum number. For example, the number of orbitals corresponding to $l = 1$ are $2 \times 1 + 1 \Rightarrow 3$. So, there are three possible values of magnetic quantum numbers that are $- 1,\,0,\, + 1$.