Objective question (only one correct).
i. The simplest formula of a compound containing 50% of element `A` (atomic mass 10) and 50% of element `B` (atomic mass 20) is:
a. `AB` b. `A_(2) B` c. `A_(2) B_(3)` d. `AB_(3)`

Explanation

To find the simplest formula of a compound containing 50% of element A (atomic mass 10) and 50% of element B (atomic mass 20), we can follow these steps:

### Step 1: Assume a Total Mass of the Compound
Assume the total mass of the compound is 100 grams. This simplifies the calculation since we can directly use the percentages.

### Step 2: Calculate the Mass of Each Element
- Since the compound is 50% A and 50% B:
- Mass of A = 50% of 100 g = 50 g
- Mass of B = 50% of 100 g = 50 g

### Step 3: Calculate the Moles of Each Element
- Moles of A = Mass of A / Atomic mass of A
\[ \text{Moles of A} = \frac{50 \text{ g}}{10 \text{ g/mol}} = 5 \text{ moles} \]

- Moles of B = Mass of B / Atomic mass of B
\[ \text{Moles of B} = \frac{50 \text{ g}}{20 \text{ g/mol}} = 2.5 \text{ moles} \]

### Step 4: Determine the Simplest Ratio
- The ratio of moles of A to moles of B is:
\[ \text{Ratio} = \frac{5}{2.5} = 2 \]
- Therefore, the simplest ratio of A to B is 2:1.

### Step 5: Write the Empirical Formula
- Based on the simplest ratio, the empirical formula can be written as:
\[ \text{Empirical formula} = A_2B \]

### Conclusion
The simplest formula of the compound is \( A_2B \).

### Answer
**Option b: \( A_2B \)**

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