Question

An electron is in one of the 3d orbitals. Give the possible values of n, l and ${m_l}$ for this electron.

Answer 1

Hint: The value ‘n’ designates the principal shell in which the electron is entering, The value of ‘l’ can be calculated from (n - 1). And further, the value of ‘${m_l}$’ which is a magnetic quantum number can be from +l to -l.

Complete step by step answer:
The electron can be defined as the subatomic particle which has negative charge. The electron is assumed to be present in shells around the nucleus in an atom.
First, let us understand what is n, l and ${m_l}$values.
The ‘n’ alphabet is used to describe the Principal quantum number. These designate the main shell in which the electron entered in an atom. Its value can be any integer with a positive value starting from 1.
The ‘l’ alphabet is used to describe the Azimuthal quantum number. These describe the shape of the given orbital. The value of azimuthal quantum number is obtained from principal quantum number. Its value can be obtained as-
‘l’ = n - 1
The ‘${m_l}$’ alphabet is used to describe the magnetic quantum number. These describe the total number of orbitals in a sub shell and their orientation. Its value can be obtained from the azimuthal quantum number. The value can be from +l to -l.
Now, the electron enters the 3d orbital.
The 3 indicated the principal quantum number. So, n = 3.
We know for n = 3 ; l = 3 - 1
‘l’ = 2
So, l can be 0, 1, 2.
For d, l = 2.
And ${m_l}$= +l to -l
So, ${m_l}$= +2, +1, 0, -1, -2.
So, the value of ${m_l}$can be any from +2 to -2.

Note: For l, we have fixed values. If l = 0; then s orbital
l = 1 ; then p orbital
l = 2 ; then d orbital
l = 3 ; then f orbital
l = 4 ; then g orbitals
The azimuthal quantum number can also be known as orbital angular momentum quantum number.