Introduction
In this problem, we are given the percentage composition of magnesium in an alloy and asked to determine how many atoms of magnesium are present in 1.00g of the alloy.

Given Information
- Percentage composition of Mg in the alloy = 24%
- Mass of the alloy = 1.00g

Solution
To determine the number of atoms of magnesium in 1.00g of the alloy, we need to follow the following steps:

Step 1: Calculate the mass of magnesium in 1.00g of alloy
- Mass of magnesium in 1.00g of alloy = 24% of 1.00g
- Mass of magnesium in 1.00g of alloy = 0.24g

Step 2: Convert the mass of magnesium to moles of magnesium
- The molar mass of magnesium is 24.31 g/mol
- Number of moles of magnesium = Mass of magnesium in grams / Molar mass of magnesium
- Number of moles of magnesium = 0.24g / 24.31 g/mol
- Number of moles of magnesium = 0.00988 mol

Step 3: Convert moles of magnesium to number of atoms of magnesium
- Avogadro's number is the number of atoms in one mole of any substance and is equal to 6.022 x 10^23 atoms/mol.
- Number of atoms of magnesium = Number of moles of magnesium x Avogadro's number
- Number of atoms of magnesium = 0.00988 mol x 6.022 x 10^23 atoms/mol
- Number of atoms of magnesium = 5.95 x 10^21 atoms

Therefore, 1.00g of the alloy contains 5.95 x 10^21 atoms of magnesium.

Conclusion
In conclusion, we have determined that there are 5.95 x 10^21 atoms of magnesium in 1.00g of the alloy with a 24% composition of magnesium.