0. Which of the following orbital diagrams are allowed, and which are not by the Pauli Exclusion Principle? Explain for those that are not and write the electronle contiguration for those that are allowed ( 8 marks) i. $$ \frac{11}{1 \mathrm{~s}} \frac{1}{2 \mathrm{~s}} \frac{1111}{20} $$ ii. $$ \frac{11}{1 s} \quad \frac{11}{2 s} \quad \frac{11}{2 p} 11 $$ iii. $$ \frac{11}{ ext { Is }} \quad \frac{11}{2 s} \quad \frac{41}{2 p} 11 $$ iv. $$ \frac{11}{1 \mathrm{~s}} \quad \frac{111}{2 \mathrm{~s}} \frac{11}{2 \mathrm{p}} $$

Question

0. Which of the following orbital diagrams are allowed, and which are not by the Pauli Exclusion Principle? Explain for those that are not and write the electronle contiguration for those that are allowed ( 8 marks) i. $$ \frac{11}{1 \mathrm{~s}} \frac{1}{2 \mathrm{~s}} \frac{1111}{20} $$ ii. $$ \frac{11}{1 s} \quad \frac{11}{2 s} \quad \frac{11}{2 p} 11 $$ iii. $$ \frac{11}{	ext { Is }} \quad \frac{11}{2 s} \quad \frac{41}{2 p} 11 $$ iv. $$ \frac{11}{1 \mathrm{~s}} \quad \frac{111}{2 \mathrm{~s}} \frac{11}{2 \mathrm{p}} $$

UpStudy AI · Accepted Answer

**i. Analysis**

- In the 1s orbital the diagram shows “$$11$$” meaning two electrons with opposite spins. This is allowed.
- In the 2s orbital the diagram shows “$$1$$” which means one electron; no violation here.
- In the 2p orbitals the diagram shows “$$1111$$”. Since the 2p subshell has three orbitals, four electrons must be arranged so that one orbital gets a pair (with opposite spins) and the other two orbitals each get one electron. This is allowed by the Pauli exclusion principle because no orbital has more than two electrons and any orbital with two electrons has opposite spins.

Thus, diagram (i) is allowed and the electron configuration is  
$$
1s^2\, 2s^1\, 2p^4.
$$

**ii. Analysis**

- The 1s orbital shows “$$11$$” so there are two electrons (one up, one down). Allowed.
- The 2s orbital shows “$$11$$” so there are two electrons (with opposite spins). Allowed.
- In the 2p subshell the diagram shows “$$11$$ 11”. In many typical orbital‐diagrams the two rows represent the two possible spin directions. In this case the two electrons in the 2p subshell are each in different orbitals (or if one orbital already has an electron, the added electron goes into an empty orbital or pairs with the opposite spin). Since only two electrons are being drawn in the 2p orbitals, there is no violation (recall that a p subshell has three orbitals available, so two electrons can be accommodated without forcing a same–spin pairing in the same orbital).

Thus, diagram (ii) is allowed and the electron configuration is  
$$
1s^2\, 2s^2\, 2p^2.
$$

**iii. Analysis**

- The 1s and 2s orbitals are shown as “$$11$$” each, so each contains two electrons, which is acceptable.
- In the 2p subshell, however, the diagram shows “$$41$$ 11”. (One way to interpret this is that in the top row there are 4 electrons and in the bottom row there are 1 electron.) Because the top row represents electrons with one spin (say “up‐spin”), and the 2p subshell has only three orbitals, placing 4 electrons with the same spin forces at least one orbital to contain two electrons with the same spin. This is forbidden by the Pauli exclusion principle.

Thus, diagram (iii) is not allowed because an orbital cannot have two electrons with identical spin.

**iv. Analysis**

- In the 1s orbital the diagram shows “$$11$$” so there are two electrons; this is allowed.
- In the 2s orbital the diagram shows “$$111$$” meaning three electrons are being placed in a single s orbital. Since an s orbital can hold at most two electrons (which must have opposite spins), this diagram violates the Pauli exclusion principle.
- (The 2p orbital shows “$$11$$” but the error in the 2s orbital is already enough to rule out the entire diagram.)

Thus, diagram (iv) is not allowed because the 2s orbital is over‐filled.

---

**Summary of Answers**

- Diagram (i) is allowed:  
  Electron configuration:  
  $$
  1s^2\, 2s^1\, 2p^4.
  $$
- Diagram (ii) is allowed:  
  Electron configuration:  
  $$
  1s^2\, 2s^2\, 2p^2.
  $$
- Diagram (iii) is not allowed because in the 2p subshell there are four electrons of the same spin in only three orbitals.
- Diagram (iv) is not allowed because the 2s orbital has three electrons.
**Allowed Orbital Diagrams and Electron Configurations** - **Diagram (i):** - Allowed - Electron Configuration: $$1s^2\, 2s^1\, 2p^4$$ - **Diagram (ii):** - Allowed - Electron Configuration: $$1s^2\, 2s^2\, 2p^2$$ - **Diagram (iii):** - Not Allowed - Reason: 2p subshell has four electrons of the same spin, violating the Pauli Exclusion Principle. - **Diagram (iv):** - Not Allowed - Reason: 2s orbital has three electrons, exceeding the maximum of two allowed. **Summary:** - Diagrams (i) and (ii) are allowed with the given electron configurations. - Diagrams (iii) and (iv) are not allowed due to violations of the Pauli Exclusion Principle.

Which of the following orbital diagrams are allowed, and which are not by the Pauli Exclusion Principle? Explain for those that are not and write the electronle contiguration for those that are allowed ( 8 marks)
i.
ii.
iii.
iv.

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Which of the following orbital diagrams are allowed, and which are not by the Pauli Exclusion Principle? Explain for those that are not and write the electronle contiguration for those that are allowed ( 8 marks) i. ii. iii. iv.