To determine which statement about halogens is correct, let's analyze each statement step by step.
### Step 1: Analyze the First Statement
**Statement:** All are diatomic and form univalent ions.
- **Explanation:** Halogens (F, Cl, Br, I) exist as diatomic molecules (e.g., F2, Cl2, Br2, I2) in their elemental form. They typically form univalent ions (e.g., F-, Cl-, Br-, I-) because they have five electrons in their outer p subshell (ns²np⁵) and can gain one electron to achieve a stable octet configuration.
**Conclusion:** This statement is correct.
### Step 2: Analyze the Second Statement
**Statement:** All are capable of exhibiting several oxidation states.
- **Explanation:** While bromine and iodine can exhibit multiple oxidation states (e.g., -1, 0, +1, +3, +5, +7), fluorine only exhibits one oxidation state, which is -1. Therefore, not all halogens can exhibit several oxidation states.
**Conclusion:** This statement is incorrect.
### Step 3: Analyze the Third Statement
**Statement:** All are diatomic and form divalent ions.
- **Explanation:** While halogens are diatomic, they do not form divalent ions. They typically form univalent ions as mentioned earlier.
**Conclusion:** This statement is incorrect.
### Step 4: Analyze the Fourth Statement
**Statement:** They can mutually displace each other from the solution of their compounds with metals.
- **Explanation:** In the halogen group, a more reactive halogen can displace a less reactive halogen from its compound. However, a halogen lower in the group cannot displace a halogen higher in the group. For example, iodine cannot displace fluorine from sodium fluoride.
**Conclusion:** This statement is incorrect.
### Final Conclusion
The only correct statement about halogens is the **first statement**: "All are diatomic and form univalent ions."
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