Question

The number of radial nodes in 3p orbital is

Answer 1

Hint:A point or plane of an orbital where the electron density of the electron of an orbital is zero is called a node. Nodes can be two types; one is a radial node and another one is an angular node. To find out the node, the concept of quantum number should be known.

Formula used: \[(n - l - 1)\]

Complete step by step answer:
Quantum numbers are characteristic quantities that are used to describe the various properties of an electron in an atom-like position, energy, or spin of the electrons. There are four quantum numbers namely, principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number.
Now for an orbital, the total number of nodes is \[(n - 1)\] . Where n is the principal quantum number. The principal quantum numbers of the shells are, for K shell is 1, for L is 2, for M shell is 3, for N shell is 4, etc. it cannot be fraction number.
Now the number of angular nodes is equal to the azimuthal quantum number denoted by ‘l’.
Therefore, the total number of radial nodes is, \[(n - l - 1)\] .
Now, for 3p orbital, the value of n is 3, and the azimuthal quantum number is 1. Therefore, the number of radial node is,
 \[
  (n - l - 1) \\
   = (3 - 1 - 1) \\
 \]
=1
So, the number of radial nodes in the 3p orbital is 1.

Additional information:
The possible values of four quantum numbers are,
Principle quantum number (n) where the value is, \[n = 1,2,3,4...\] any integer.
Azimuthal quantum number (l) the value is, \[l = 0\,to\,(n - 1)\]
Example: for the value of \[n = 3\] the value of I=0.1.2 , Where,\[{\text{l = 0}}\]for s orbital, \[l = 1\] for p orbital\[{\text{l = 2}}\]for d orbital, \[l = 3\] for f orbital.
Magnetic quantum number (m): the value is \[m = - lto + l\]
Example: for the value \[l = 3\]
M=-3,-2,-1,0,+1,+2,+3
Spin quantum number(s): the value is \[ \pm \dfrac{1}{2}\] . for every value of m.
Example: for M=-3,-2,-1,0,+1,+2,+3

 \[s = \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}, \pm \dfrac{1}{2}\]
Where the + sign means clockwise spin rotation of electron and the – sign means anti-clockwise spin rotation of electrons.

Note:
The Quantum mechanical model of the atom uses complex shapes of orbitals, volumes of space in which there is likely to be an electron. It states that an electron is not only a particle but has a wave character.In 1926 Erwin Schrodinger took the Bohr atom model one step further. He used mathematical positions. This atomic model is known as a quantum mechanical model of the atom. This model is based upon the dual nature of the electron, i.e. the electron is not only a particle but has a wave character. The wave character of the electron has particle significance since its wavelength is easily observed in the electromagnetic spectrum.