Question

Which of the following orbitals have no spherical nodes?
THIS QUESTION HAS MULTIPLE CORRECT OPTIONS
A. 1s
B. 2s
C. 2p
D. 3p

Answer 1

Hint: Number of spherical nodes in an orbit can be calculated by n−l−1. Where n is the principal quantum number, and l is the angular momentum quantum number.


Complete answer:
In this question we have asked, which of the following orbital does not have spherical nodes. So, A spherical node is known as a radial node and it can be calculated by n−l−1. Where n is the principal quantum number, and l is the angular momentum quantum number. The angular momentum quantum number or l can be described as the shape of the orbital that an electron occupies and it can be calculated by $n - 1$, where n is 1 for s, 2 for p, 3 for d, and so on and l is 0 for s, 1 for p, 2 for d and so on.
1. So, our first option is 1s, in which n=1 and l=0
So, no. of spherical node$= n-l-1= 1-0-1= 0$
So, 1s have 0 spherical nodes.

2. Our second option is 2s, in which n=2 and l=0
So, no. of spherical node$= n-l-1= 2-0-1= 1$
So, 2s have 1 spherical node.

3. Our second option is 2p, in which n=2 and l=1
So, no. of spherical node$= n-l-1= 2-1-1= 0$
So, 2p has 0 spherical nodes.

4. Our second option is 3p, in which n=3 and l=1
So, no. of spherical node$= n-l-1= 3-1-1= 1$
So, 2s have 1 spherical node.
So, 1s and 2p orbitals have no spherical nodes.

And the correct options will be A and C.

Note: As we already mentioned that no. of spherical nodes $= n-l-1$ and $l= n-1$. Do not confuse between the n. The meaning of n in both formulas is different. In formula (1), n is the number of valence shells. While n in the second formula is principal quantum no. Which is 1 for s, 2 for p, and so on.