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 .