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. `(y)/(2)`
B. `(y)/(4)`
C. y
D. 2y

Answer

To solve the problem step by step, we will first determine the number of moles of elements A and B, and then calculate the number of atoms based on the provided information.

### Step 1: Determine the number of moles of element A
The number of moles (n) of an element can be calculated using the formula:
\[ n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

For element A:
- Given mass = \( x \) g
- Atomic weight (molar mass) of A = 40 g/mol

So, the number of moles of A is:
\[ n_A = \frac{x}{40} \]

### Step 2: Calculate the number of atoms in element A
The number of atoms (N) can be calculated using Avogadro's number (\( N_A = 6.022 \times 10^{23} \) atoms/mol):
\[ N_A = n \times N_A \]

Thus, the number of atoms in \( x \) grams of A is:
\[ N_A = \frac{x}{40} \times 6.022 \times 10^{23} \]

According to the problem, this is equal to \( y \):
\[ \frac{x}{40} \times 6.022 \times 10^{23} = y \]

### Step 3: Determine the number of moles of element B
For element B:
- Given mass = \( 2x \) g
- Atomic weight (molar mass) of B = 80 g/mol

So, the number of moles of B is:
\[ n_B = \frac{2x}{80} = \frac{x}{40} \]

### Step 4: Calculate the number of atoms in element B
Using the same method as before, the number of atoms in \( 2x \) grams of B is:
\[ N_B = n_B \times N_A = \frac{x}{40} \times 6.022 \times 10^{23} \]

### Step 5: Relate the number of atoms in B to the number of atoms in A
From Step 2, we have:
\[ N_A = y \]
From Step 4, we have:
\[ N_B = \frac{x}{40} \times 6.022 \times 10^{23} \]

Since \( n_B = n_A \), we can conclude:
\[ N_B = y \]

### Conclusion
Thus, the number of atoms present in \( 2x \) grams of B is equal to \( y \).

### Final Answer
The number of atoms present in \( 2x \) grams of B is \( y \).

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