Which orbital notation does not have spherical node______.

• a. n = 2, l = 0
• b. n = 2, l = 1
• c. n = 3, l = 0
• d. n = 3, l = 1

To determine which orbital notation does not have a spherical node, we need to understand the quantum numbers involved.

Quantum Numbers Explained

Each orbital is defined by three quantum numbers: n (principal quantum number), l (azimuthal quantum number), and m (magnetic quantum number). The value of l indicates the shape of the orbital:

• l = 0: s orbital (spherical)
• l = 1: p orbital (dumbbell-shaped)
• l = 2: d orbital (clover-shaped)

Identifying Spherical Nodes

A spherical node occurs in s orbitals (where l = 0). The number of nodes is given by the formula: n - l - 1. This means:

• For n = 2, l = 0: 1 spherical node (2 - 0 - 1 = 1)
• For n = 2, l = 1: 0 spherical nodes (2 - 1 - 1 = 0)
• For n = 3, l = 0: 2 spherical nodes (3 - 0 - 1 = 2)
• For n = 3, l = 1: 1 spherical node (3 - 1 - 1 = 1)

Final Answer

The notation that does not have a spherical node is n = 2, l = 1 (option b).