Question

Calculate the total number of radial and angular nodes for 5d and 4p orbitals.
Also Determine the values of n, l and m for these orbitals.

Answer 1

Given

Orbitals 5d and 4p

To determine

• Number of radial nodes

• Number of angular nodes.

• The value of n , l and m for these orbitals.

Concepts

• Quantum number 'n' denotes the orbit . It can acquire natural values only . (1,2,3......)

• Quantum number 'l' is called azimuthal quantum number and it describes shape of the orbital.There orbital are designated specific code names like s-orbital, p-orbital ,d-orbital and f-orbital. Their values being 0,1,2 and 3 respectively. In an orbit 'n' , there are all total n orbitals and their values lies from 0 to n-1.

• The quantum number 'm' is called magnetic quantum number and describes orientation of the electron.In an orbital having value l , m lies from -l to l. Thus, for each l, there are 2l + 1 possible values.

For example : - For p-orbital (l = 1) , m has the value -1 , 0 , 1.

• Nodes are those points where probability of finding an electron is zero.

• Number of radial node is given by n - l - 1.

• Number of angular node is given by l

• Total number of nodes for an orbital is (n-1).

Solutions

5d

n = 5 , l = 2 ( For d orbital l = 2) , m can be -2, -1, 0, 1 ,2

Number of radial node = n - l - 1 = 5 - 2 - 1 = 2 Ans.

Number of angular node = l = 2.

4p

n = 4 , l = 1 ( For p orbital l = 1) , m can be -1, 0, 1 ,

Number of radial node = n - l - 1 = 4 - 1 - 1 = 2 Ans.

Number of angular node = l = 1.