Question

The total number of radial and angular nodes present in \[{\text{5f}}\]orbital are ________.

Answer 1

Hint: Each orbital in an atom is designed by a set of three quantum numbers and each electron is designated by a set of four quantum numbers. Knowing the quantum numbers helps us to find the number of radial and angular nodes.

Complete step by step answer:
The most important quantum number that determines the energy of an atom is the principal quantum number. It is denoted by the letter ‘n’. it can have the values 1,2,3 etc. A s the value of ‘n’ increases, the electron goes farther away from the nucleus and its energy decreases.
The next important quantum number is the azimuthal quantum number denoted by the letter ‘l’. It also determines the shape of the orbital in which the electron is located. This gives us the number of nodes present in an orbital as an orbital is the space around the nucleus where the probability of finding the electron is maximum. The number of subshells within a principal shell is determined by the value of ‘n’ for that level. Thus, ‘l’ may have all possible whole number values from 0 to \[{\text{n - 1}}\].
Here we have the \[{\text{5f}}\] orbital which has the value of principal quantum number ‘n’ as 5 and the value of azimuthal quantum number as 3 for f subshell. Therefore, the number of radial and angular nodes are given by;
No. of angular nodes= l= 3
No. of radial nodes= \[{\text{n - l - 1}}\;{\text{ = 5 - 3 - 1 = 2}}\]
Therefore, the number of radial nodes is equal to 1 and the number of angular nodes is equal to 3.

Additional Information:
In order to understand the distribution of electrons in a given volume of space about the nucleus we need to know the wave functions. An orbital wave function can be written as the product of radial and angular function.

Note: As the distribution of electrons in a given space is given by the orbital wave function which includes the angular and radial functions, the radial part tells us about the size of the orbital and the angular part tells us about the shape of the orbital.