Question

How many spherical nodes does a 3d orbital have?
1) 0
2) 1
3) 2
4) 3

Answer 1

A 3d orbital has 0 spherical nodes, as determined by the formula for calculating nodes which is nodes = n - l - 1, where n is the principal quantum number and l is the angular momentum quantum number.

Step-by-step explanation:

The question pertains to the number of spherical nodes in a 3d orbital. A spherical node is an area in an orbital where there is a zero probability of finding an electron. According to the quantum mechanical model of the atom, d orbitals, which are represented by a quantum number l = 2, have complex shapes that incorporate nodal surfaces.

For any d orbital (which corresponds to l = 2), we can calculate the number of nodes using the formula: nodes = n - l - 1, where n is the principal quantum number and l is the angular momentum quantum number. For a 3d orbital, where n=3 and l=2, the calculation would be: nodes = 3 - 2 - 1, resulting in 0 spherical nodes.

Therefore, a 3d orbital has 0 spherical nodes.