Boron of highest purity `(~99.9%)` is obtained by

Options

A. reduction of `B_(2)O_(2)` by `Mg`.
B. electrolysis of fused tetrafluoroborates `(KBF_(4))` in molten `KF`.
C. reduction of `BCl_(3)` with `H_(2)` at `1270 K`.
D. thermal decomposition of boranes at `1173 K`.

Explanation

To determine how boron of the highest purity (~99.9%) is obtained, we need to analyze the given options step by step.

### Step 1: Analyze the Options
We have four options to consider:
1. Reduction of boron oxide by magnesium.
2. Electrolysis of fused tetrafluoroborates in molten KF.
3. Reduction of boron trichloride with hydrogen at 1270 Kelvin.
4. Thermal decomposition of borane at 1173 Kelvin.

### Step 2: Evaluate Option 1
- **Reduction of Boron Oxide by Magnesium**:
- Boron oxide (B2O3) can be reduced by magnesium to produce boron and magnesium oxide (MgO).
- However, this method does not yield pure boron, as the product will contain impurities from magnesium oxide.

**Hint**: Consider the purity of the product when evaluating reduction reactions.

### Step 3: Evaluate Option 2
- **Electrolysis of Fused Tetrafluoroborates**:
- This involves the electrolysis of potassium tetrafluoroborate (KBF4) in molten KF.
- While this method can produce boron, it may still contain small amounts of KF as impurities.

**Hint**: Think about the presence of impurities during electrolysis processes.

### Step 4: Evaluate Option 3
- **Reduction of Boron Trichloride with Hydrogen**:
- In this method, boron trichloride (BCl3) is reduced by hydrogen at a high temperature (1270 Kelvin).
- The reaction produces boron and hydrochloric acid (HCl). The balanced equation shows that HCl can be distilled away, leading to a very high purity of boron (around 99.9%).

**Hint**: High temperatures and the ability to remove byproducts can lead to higher purity.

### Step 5: Evaluate Option 4
- **Thermal Decomposition of Borane**:
- This process involves heating borane (BH3), which can release hydrogen gas.
- However, the boron produced may still contain hydrogen as an impurity, leading to lower purity.

**Hint**: Consider the nature of byproducts in thermal decomposition reactions.

### Conclusion
After evaluating all options, the best method for obtaining boron of the highest purity (~99.9%) is:

**Option C: Reduction of boron trichloride with hydrogen at 1270 Kelvin.**

This method effectively produces pure boron while allowing the removal of hydrochloric acid, thus achieving the desired purity.