b. 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 electroni configuration for those that are allowed (8 marks). i. $$ \frac{\uparrow \downarrow}{1 \mathrm{~s}} \quad \frac{\uparrow}{2 \mathrm{~s}} \quad \frac{\uparrow \uparrow \uparrow \downarrow}{2 p} $$ ii. $$ \frac{\uparrow \downarrow}{1 \mathrm{~s}} \quad \frac{\uparrow \downarrow}{2 \mathrm{~s}} $$ iii. $$ \frac{\uparrow \downarrow}{2 p} $$ $$ \frac{\uparrow \downarrow}{1 \mathrm{~s}} $$ is $$ \frac{\uparrow \downarrow}{2 p} $$ iv. $$ \frac{\uparrow \downarrow}{1 \downarrow} $$ $$ \frac{\uparrow \downarrow \uparrow}{2 \mathrm{~s}} $$ $$ \frac{\uparrow \downarrow}{2 p} $$

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To determine which of the given orbital diagrams are allowed according to the Pauli Exclusion Principle, we need to remember that this principle states that no two electrons in an atom can have the same set of four quantum numbers. In simpler terms, an orbital can hold a maximum of two electrons, and they must have opposite spins.

Let's analyze each of the provided diagrams:

### i. 
$$
\frac{\uparrow \downarrow}{1 \mathrm{~s}} \quad \frac{\uparrow}{2 \mathrm{~s}} \quad \frac{\uparrow \uparrow \uparrow \downarrow}{2 p}
$$
- **Analysis**: 
  - The $$1s$$ orbital has 2 electrons with opposite spins, which is allowed.
  - The $$2s$$ orbital has 1 electron, which is allowed.
  - The $$2p$$ orbital has 4 electrons, which is **not allowed** because it exceeds the maximum of 6 electrons (2 per orbital with opposite spins).
  
- **Conclusion**: **Not allowed** due to the $$2p$$ orbital.

### ii. 
$$
\frac{\uparrow \downarrow}{1 \mathrm{~s}} \quad \frac{\uparrow \downarrow}{2 \mathrm{~s}}
$$
- **Analysis**: 
  - The $$1s$$ orbital has 2 electrons with opposite spins, which is allowed.
  - The $$2s$$ orbital also has 2 electrons with opposite spins, which is allowed.
  
- **Conclusion**: **Allowed**. The electron configuration is $$1s^2 2s^2$$.

### iii. 
$$
\frac{\uparrow \downarrow}{2 p} \quad \frac{\uparrow \downarrow}{1 \mathrm{~s}}
$$
- **Analysis**: 
  - The $$2p$$ orbital has 2 electrons with opposite spins, which is allowed.
  - The $$1s$$ orbital has 2 electrons with opposite spins, which is also allowed.
  
- **Conclusion**: **Allowed**. The electron configuration is $$1s^2 2p^2$$.

### iv. 
$$
\frac{\uparrow \downarrow}{1 \downarrow} \quad \frac{\uparrow \downarrow \uparrow}{2 \mathrm{~s}} \quad \frac{\uparrow \downarrow}{2 p}
$$
- **Analysis**: 
  - The notation $$1 \downarrow$$ is unclear, but if it implies that there is an electron with spin down in the $$1s$$ orbital, it would mean that the $$1s$$ orbital is not fully occupied (which is allowed).
  - The $$2s$$ orbital has 3 electrons, which is **not allowed** because it exceeds the maximum of 2 electrons.
  - The $$2p$$ orbital has 2 electrons with opposite spins, which is allowed.
  
- **Conclusion**: **Not allowed** due to the $$2s$$ orbital.

### Summary:
- **i**: Not allowed (due to $$2p$$ orbital).
- **ii**: Allowed, configuration: $$1s^2 2s^2$$.
- **iii**: Allowed, configuration: $$1s^2 2p^2$$.
- **iv**: Not allowed (due to $$2s$$ orbital).
- **i**: Not allowed (too many electrons in $$2p$$). - **ii**: Allowed, configuration: $$1s^2 2s^2$$. - **iii**: Allowed, configuration: $$1s^2 2p^2$$. - **iv**: Not allowed (too many electrons in $$2s$$).

b. 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 electroni
configuration for those that are allowed (8 marks).
i.
ii.
iii.

is

iv.

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b. 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 electroni configuration for those that are allowed (8 marks). i. ii. iii. is iv.