A' on heating at `700^(@)C` in air gives a white infusible amorphous powder (B) which is decomposed when heated in the currect of steam to give white powder 'C' and a gas 'D'.'D' turns red litmus blue and in aqueous solution , gives reddish brown ppt with `K_(2)HgI_(4)`. compound 'C on strong heating gives 'E.
'B' is

Options

A. `BN`
B. `B_(2)O_(3)`
C. `SiO_(2)`
D. `P_(4)O_(10)`

Explanation

To solve the problem step by step, we will analyze the information given in the question and deduce the compounds involved.

### Step 1: Identify Compound A
The question states that compound A, when heated in air at 700°C, produces a white infusible amorphous powder B. The most likely candidate for compound A is **Boron (B)**, as it reacts with oxygen in the air to form boron oxide.

**Hint:** Consider elements that can react with oxygen to form oxides at high temperatures.

### Step 2: Determine Compound B
When boron (A) is heated in air, it forms **Boron Trioxide (B2O3)**, which is a white infusible amorphous powder. Therefore, compound B is **Boron Trioxide (B2O3)**.

**Hint:** Think about the oxides formed by elements when they react with oxygen.

### Step 3: Reaction of Compound B with Steam
Next, compound B (B2O3) is heated in the presence of steam (water vapor). The reaction of boron trioxide with steam produces **Boric Acid (H3BO3)**, which is a white powder (C), and a gas (D).

**Hint:** Consider how oxides react with water to form acids or bases.

### Step 4: Identify Compound C
The white powder C formed in this reaction is **Boric Acid (H3BO3)**.

**Hint:** Recall the common acids formed from oxides when they react with water.

### Step 5: Identify Gas D
The gas D produced in this reaction is **Ammonia (NH3)**. The question states that D turns red litmus blue, indicating that it is basic in nature. Ammonia is a well-known basic gas.

**Hint:** Think about gases that are basic and can turn litmus paper blue.

### Step 6: Reaction of Compound C
When boric acid (C) is strongly heated, it decomposes to form **Boron Oxide (B2O3)** again, which is compound E.

**Hint:** Consider the thermal stability of acids and their decomposition products when heated.

### Conclusion
Based on the deductions made through the steps:
- **Compound A** is **Boron (B)**.
- **Compound B** is **Boron Trioxide (B2O3)**.
- **Compound C** is **Boric Acid (H3BO3)**.
- **Gas D** is **Ammonia (NH3)**.
- **Compound E** is **Boron Oxide (B2O3)**.

Thus, the final answer is that **B is Boron Trioxide (B2O3)**.