Explanation:

To solve this problem, we need to use the concept of Avogadro's number.

Avogadro's number is the number of atoms in one mole of a substance. It is equal to 6.022 × 10²³ atoms/mol.

Thus, the number of atoms in any given amount of a substance can be calculated by dividing the amount by the atomic weight of the substance and multiplying by Avogadro's number.

Using this formula, we can calculate the number of atoms present in each of the given substances:

a) 24 g of Mg
The atomic weight of Mg is 24.31 g/mol. Therefore, the number of moles in 24 g of Mg is:
24 g ÷ 24.31 g/mol = 0.9884 mol
The number of atoms in 0.9884 mol of Mg is:
0.9884 mol × 6.022 × 10²³ atoms/mol = 5.946 × 10²³ atoms

b) 8 g of Oxygen
The atomic weight of Oxygen is 16 g/mol. Therefore, the number of moles in 8 g of Oxygen is:
8 g ÷ 16 g/mol = 0.5 mol
The number of atoms in 0.5 mol of Oxygen is:
0.5 mol × 6.022 × 10²³ atoms/mol = 3.011 × 10²³ atoms

c) 32 g of Sulphur
The atomic weight of Sulphur is 32.06 g/mol. Therefore, the number of moles in 32 g of Sulphur is:
32 g ÷ 32.06 g/mol = 0.9981 mol
The number of atoms in 0.9981 mol of Sulphur is:
0.9981 mol × 6.022 × 10²³ atoms/mol = 6.011 × 10²³ atoms

d) 12 g of Carbon
The atomic weight of Carbon is 12.01 g/mol. Therefore, the number of moles in 12 g of Carbon is:
12 g ÷ 12.01 g/mol = 0.9992 mol
The number of atoms in 0.9992 mol of Carbon is:
0.9992 mol × 6.022 × 10²³ atoms/mol = 6.020 × 10²³ atoms

Therefore, the correct answer is option B, as 0.5 g-atoms of nitrogen has the same number of atoms as 8 g of Oxygen.