The atomic weights of two alements A and B are 40 and 80 reapectively. If x g of A contains y atoms, how many atoms are present in 2x g of B?

Options

A. (a)`y/2`
B. (b)`y/4`
C. (c )y
D. (d)2y

Explanation

To solve the problem, we need to determine how many atoms are present in 2x grams of element B, given the atomic weights of elements A and B and the number of atoms in x grams of A.

### Step-by-Step Solution:

1. **Identify the Atomic Weights**:
- The atomic weight of element A = 40 g/mol.
- The atomic weight of element B = 80 g/mol.

2. **Understand the Concept of Moles**:
- 1 mole of any substance contains Avogadro's number of atoms, which is approximately \(6.022 \times 10^{23}\) atoms.
- Therefore, 40 grams of element A contains \(6.022 \times 10^{23}\) atoms.

3. **Calculate the Number of Moles in x grams of A**:
- The number of moles of A in x grams can be calculated using the formula:
\[ \text{Number of moles of A} = \frac{x \text{ g}}{40 \text{ g/mol}} \]

4. **Calculate the Number of Atoms in x grams of A**:
- The number of atoms in x grams of A is given as y, which can be expressed as:
\[ y = \left(\frac{x}{40}\right) \times 6.022 \times 10^{23} \]

5. **Calculate the Number of Moles in 2x grams of B**:
- The number of moles of B in 2x grams can be calculated using the formula:
\[ \text{Number of moles of B} = \frac{2x \text{ g}}{80 \text{ g/mol}} = \frac{x}{40} \]

6. **Calculate the Number of Atoms in 2x grams of B**:
- The number of atoms in 2x grams of B can be calculated as:
\[ \text{Number of atoms in 2x grams of B} = \left(\frac{x}{40}\right) \times 6.022 \times 10^{23} \]

7. **Compare the Number of Atoms**:
- From the calculations, we see that the number of atoms in 2x grams of B is equal to the number of atoms in x grams of A, which is y.
- Therefore, the number of atoms in 2x grams of B is also y.

### Final Answer:
The number of atoms present in 2x grams of B is **y**.