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Zorluk: KolayElectronic Configuration, Orbitals, and Quantum Rules

Arrange the following atomic subshells in order of increasing energy according to the Aufbau principle ((n+l)(n+l) rule):

  1. 13s3s
  2. 23p3p
  3. 34s4s
  4. 43d3d

Cevap

The correct order of increasing orbital energy is 3s→3p→4s→3d3s \rightarrow 3p \rightarrow 4s \rightarrow 3d.
By applying the (n+l)(n+l) rule (Madelung's rule) derived from the Aufbau principle, subshells fill in order of increasing (n+l)(n+l) energy sum. Calculating these values yields: 3s3s (3+0=33+0=3), 3p3p (3+1=43+1=4), 4s4s (4+0=44+0=4), and 3d3d (3+2=53+2=5). For subshells with equal sums (3p3p and 4s4s), the one with the smaller principal quantum number nn is lower in energy (3p3p with n=3n=3 is lower than 4s4s with n=4n=4). Therefore, the correct sequence from lowest to highest energy is 3s→3p→4s→3d3s \rightarrow 3p \rightarrow 4s \rightarrow 3d.

Adım Adım Çözüm

1
Determine the (n+l)(n+l) value for each subshell
For 3s3s: 3+0=33+0 = 3. For 3p3p: 3+1=43+1 = 4. For 4s4s: 4+0=44+0 = 4. For 3d3d: 3+2=53+2 = 5.
According to the Aufbau principle and the (n+l)(n+l) rule, orbitals fill in order of increasing (n+l)(n+l) energy values.
2
Compare subshells with identical (n+l)(n+l) values
Both 3p3p and 4s4s have (n+l)=4(n+l) = 4. Since 3p3p has a smaller principal quantum number (n=3n=3 compared to n=4n=4), 3p3p is lower in energy than 4s4s.
When two orbitals have the same (n+l)(n+l) value, the orbital with the lower principal quantum number nn has lower energy.
3
Sequence the subshells from lowest to highest energy
The final sequence is 3s<3p<4s<3d3s < 3p < 4s < 3d.
Sorting by (n+l)(n+l) sum first, then by nn value for ties, yields the correct Aufbau order.

Anahtar Kavram

Aufbau Principle and the (n+l) Rule
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Konular

Electronic Configuration, Orbitals, and Quantum Rules

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