1. Identify the orbitals from the given quantum numbers

For a given azimuthal quantum number $l$:

• $l=0 \Rightarrow s$
• $l=1 \Rightarrow p$
• $l=2 \Rightarrow d$

So the given electrons correspond to:

• (a) $n=4, l=1 \Rightarrow 4p$
• (b) $n=4, l=0 \Rightarrow 4s$
• (c) $n=3, l=2 \Rightarrow 3d$
• (d) $n=3, l=1 \Rightarrow 3p$

2. Use the $(n+l)$ rule to compare energies

For multi-electron atoms, orbital energy increases with increasing value of $(n+l)$. If two orbitals have the same $(n+l)$ value, then the one with smaller $n$ has lower energy.

Now calculate $n+l$ for each:

• (a) $4p: n+l = 4+1 = 5$
• (b) $4s: n+l = 4+0 = 4$
• (c) $3d: n+l = 3+2 = 5$
• (d) $3p: n+l = 3+1 = 4$

3. Order orbitals with same $(n+l)$

• Between $3p$ and $4s$, both have $n+l=4$. Since smaller $n$ means lower energy: $3p < 4s$ So, $(d) < (b)$

• Between $3d$ and $4p$, both have $n+l=5$. Since smaller $n$ means lower energy: $3d < 4p$ So, $(c) < (a)$

4. Combine the full increasing order

All orbitals with $n+l=4$ are lower in energy than those with $n+l=5$. Thus, $3p < 4s < 3d < 4p$

In terms of the labels: $(d) < (b) < (c) < (a)$

5. Match with the options

This corresponds to Option B.

6. Compare with stored correct answer

Stored correct answer = B

My derived answer = B

So, the answer agrees with the stored correct answer.