Question

What is the total number of f orbitals in an f subshell?

Answer 1

Hint :The Azimuthal quantum number designates the subshells to which the electron belongs.it tells about the shape of the orbitals. For a given value of principal quantum number \[(n),'l'\]can have values ranging.

Complete Step By Step Answer:
Firstly a shell is determined by principal quantum number. It surrounds the nucleus. These shells are also represented by letters like K, L, M and N shell.
The Azimuthal quantum number \['l'\]can have values ranging from \[0{\text{ to n - 1}}\]the number of subshells in a principal shell is equal to the value of n example, there is only one subshell \[(l = 0)\] in the first shell \[(n = 1)\].
The subshells corresponding to different values of \[l\] are represented by the following symbols:
If value of \[l\] is \[0,1,2{\text{ and 3}}\]then the subshell notation are s, p, d and f respectively.
The Magnetic orbital quantum number \['{m_l}'\]determines the number of preferred orientations of the orbitals in a subshell. We can also say that it gives the total number of orbitals present in a given subshell.
Formula to find orbital: \[2l + 1\]
For a given subshell there are \[2l + 1\] values of \['{m_l}'\]which are possible.
For an electron belonging to\[(l = 3)\]subshell that is f subshell, there are \[(2l + 1){m_l}\]value that is $ + 3, + 2, + 1,0, - 1, - 2, - 3$ values. Therefore as there are$7{\text{ '}}{m_l}'$values, therefore $7{\text{ }}$numbers of orbitals are present in \[(l = 3)\]subshell. Moreover the number of ${m_l}$values range from $ + l{\text{ to - }}l$ including $0$.
So, ${m_l}$values are $ + 3, + 2, + 1,0, - 1, - 2, - 3$ which makes total of 7 orbitals of f subshell.

Note :
The Magnetic orbital quantum number \['{m_l}'\] explained the splitting of a single spectral line of hydrogen atom into a number of closely spaced lines in the presence of electric(stark effect) and magnetic field .