To determine which group of elements can have both positive and negative oxidation states, we will analyze each of the provided options step by step.
### Step 1: Analyze the First Option - Hydrogen, Fluorine, and Oxygen
- **Hydrogen (H)**: The electronic configuration is 1s¹. Hydrogen can lose one electron to form H⁺ (oxidation state +1) or gain one electron to form H⁻ (oxidation state -1).
- **Fluorine (F)**: The electronic configuration is 1s² 2s² 2p⁵. Fluorine is highly electronegative and typically has an oxidation state of -1 (as in HF) and does not exhibit positive oxidation states.
- **Oxygen (O)**: The electronic configuration is 1s² 2s² 2p⁴. Oxygen generally has an oxidation state of -2 (as in H₂O) but can also exhibit a positive oxidation state in compounds like OF₂ (+2).
**Conclusion for Option 1**: Hydrogen can have both +1 and -1, Oxygen can have -2 and +2, but Fluorine only has -1. Therefore, this group does not satisfy the condition.
### Step 2: Analyze the Second Option - Sodium, Magnesium, and Aluminium
- **Sodium (Na)**: The electronic configuration is 1s² 2s² 2p⁶ 3s¹. Sodium typically has an oxidation state of +1.
- **Magnesium (Mg)**: The electronic configuration is 1s² 2s² 2p⁶ 3s². Magnesium typically has an oxidation state of +2.
- **Aluminium (Al)**: The electronic configuration is 1s² 2s² 2p⁶ 3s² 3p¹. Aluminium can have oxidation states of +1, +2, and +3.
**Conclusion for Option 2**: Sodium and Magnesium only exhibit positive oxidation states, while Aluminium can show +1, +2, and +3. This group does not satisfy the condition of having both positive and negative oxidation states.
### Step 3: Analyze the Third Option - Chlorine, Bromine, and Iodine
- **Chlorine (Cl)**: The electronic configuration is 1s² 2s² 2p⁶ 3s² 3p⁵. Chlorine can have oxidation states of -1 (as in HCl) and +1, +3, +5, +7 in various compounds.
- **Bromine (Br)**: The electronic configuration is similar to chlorine. Bromine can exhibit oxidation states of -1, +1, +3, +5, and +7.
- **Iodine (I)**: The electronic configuration is also similar. Iodine can have oxidation states of -1, +1, +3, +5, and +7.
**Conclusion for Option 3**: All three elements can exhibit both positive and negative oxidation states. This group satisfies the condition.
### Step 4: Analyze the Fourth Option - Hydrogen, Chlorine, and Bromine
- **Hydrogen (H)**: As previously mentioned, it can have +1 and -1.
- **Chlorine (Cl)**: Can have -1 and positive oxidation states.
- **Bromine (Br)**: Can also have -1 and positive oxidation states.
**Conclusion for Option 4**: This group can also exhibit both positive and negative oxidation states.
### Final Answer
The group where elements can have both positive and negative oxidation states is **Chlorine, Bromine, and Iodine (Option 3)**.
