The number of atomic orbitals from the following having 5 radial nodes is ___________.
7 s, 7 p, 6 s, 8 p, 8 d

Solution

Chemistry ma’am · 2 steps

Radial nodes are n - l - 1, so work out that number for each orbital and count the fives.

1. The formula. An orbital has n - 1 nodes in total. Of these, l are angular, so the rest are radial.

   radial nodes = n - l - 1

   Orbital	n	l	Radial nodes n - l - 1
   7s	7	0	7 - 0 - 1 = 6
   7p	7	1	7 - 1 - 1 = 5
   6s	6	0	6 - 0 - 1 = 5
   8p	8	1	8 - 1 - 1 = 6
   8d	8	2	8 - 2 - 1 = 5

2. So. 7p, 6s and 8d each have 5 radial nodes, so the answer is 3.

The common slip: 1. Using the total node count n - 1 in place of n - l - 1 picks out only 6s and gives 1, not 3.

The idea to keep. Total nodes are n - 1. Angular nodes are l. Radial nodes are what is left, n - l - 1. Use the full formula every time and never skip the l.

Answer from the NTA final answer key. Solution by PrepWiser.