How to Find the Orbital Symbol using Radial & Angular Nodes
In the Atomic Structure chapter, understanding quantum numbers and nodes is essential for both JEE and NEET exams. A "node" is a region in space around the nucleus where the probability of finding an electron is exactly zero.
Examiners love to test this concept in two ways: either they give you the orbital symbol (like 3p or 4d) and ask for the number of nodes, OR they give you the number of nodes and ask you to reverse-engineer the exact orbital symbol. Let's learn how to do both!
Video Tutorial: Reverse-Engineering the Orbital
Watch Abhishek Sengar sir from CHEMCA instantly solve a question asking for the orbital symbol given 3 radial nodes and 2 angular nodes.
The Core Formulas
To solve any question regarding nodes, you only need to memorize two simple formulas relying on the Principal Quantum Number (n) and the Azimuthal Quantum Number (l):
s-orbital: l = 0 | p-orbital: l = 1 | d-orbital: l = 2 | f-orbital: l = 3
Solved Example from the Video
Question: What will be the symbol of an orbital that has 3 radial nodes and 2 angular nodes?
-
Find the Azimuthal Quantum Number (l):
We know: Angular Nodes = l
Given Angular Nodes = 2. Therefore, l = 2.
An l value of 2 corresponds to a d-orbital. -
Find the Principal Quantum Number (n):
Formula: Radial Nodes = n - l - 1
We know Radial Nodes = 3, and we just found l = 2.
Substitute the values: 3 = n - 2 - 1
3 = n - 3
n = 3 + 3 = 6 -
Combine for Final Symbol:
With n = 6 and orbital type d, the exact symbol is 6d.
Practice Questions for JEE & NEET
As Abhishek Sir mentioned, exam questions can be asked from both directions. Try these two variations!
Question 1 (Forward Type): Calculate the number of radial nodes, angular nodes, and total nodes for a 5p orbital.
Step-by-step Solution:
- For a 5p orbital, the quantum numbers are: n = 5 and l = 1 (since it's a p-orbital).
- Angular Nodes = l = 1
- Radial Nodes = n - l - 1 = 5 - 1 - 1 = 3
- Total Nodes = Angular + Radial = 1 + 3 = 4 (Alternatively, Total Nodes = n - 1 = 5 - 1 = 4)
Question 2 (Reverse Type): Find the symbol of the orbital which has exactly 2 radial nodes and 1 angular node.
Step-by-step Solution:
- Find l: Angular node = l = 1. This means it is a p-orbital.
- Find n: Radial nodes = n - l - 1 = 2.
- Substitute l = 1 into the equation: n - 1 - 1 = 2.
- n - 2 = 2 ⟶ n = 4.
- Answer: Since n = 4 and l = 1, the orbital symbol is 4p.
No comments:
Post a Comment