In a multielectron atom, which of the following orbitals described by three quantum numbers will have same energy in absence of electric and magnetic fields?
A. n=1, l=0, m₁=0
B. n=2, l=0, m₁=0
C. n=2, I=1, m₁=1
D. n=3, l=2, m₁=1
E. n=3, l=2, m₁=0
Choose the correct answer from the options given below:

Solution

Chemistry ma’am · 3 steps

In a multielectron atom energy depends on both n and l, so look for two orbitals that share both.

1. What sets energy. In a multielectron atom, electrons shield one another, so orbital energy depends on n and l together. The value of mₗ only gives the orientation, and without an electric or magnetic field all orientations have the same energy.

   Orbital	n	l	Subshell
   A	1	0	1s
   B	2	0	2s
   C	2	1	2p
   D	3	2	3d
   E	3	2	3d

2. Compare the pairs. B and C share n = 2 but differ in l, so 2s lies below 2p. Only D and E have the same n and the same l. They differ only in mₗ, which makes them two degenerate 3d orbitals.
3. So. D and E have the same energy, which is option (d).

The idea to keep. In hydrogen only n fixes the energy. In any multielectron atom you need the same n and the same l. A different mₗ never changes energy unless a field is applied.

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