Answer :
To find the number of g-atoms of calcium remaining after removing \( 1.2 \times 10^{19} \) atoms from an initial mass of 2 mg of calcium, follow these steps:
1. Convert the initial mass from milligrams to grams:
[tex]\[ \text{Initial mass in mg} = 2 \, \text{mg} \][/tex]
[tex]\[ \text{Initial mass in grams} = \frac{2 \, \text{mg}}{1000} = 0.002 \, \text{g} \][/tex]
2. Calculate the number of moles of calcium in the initial sample:
Given the atomic mass of calcium (\( \text{Ca} \)) is 40 g/mol,
[tex]\[ \text{Number of moles} = \frac{\text{Initial mass in grams}}{\text{Atomic mass of Ca}} = \frac{0.002 \, \text{g}}{40 \, \text{g/mol}} = 5 \times 10^{-5} \, \text{mol} \][/tex]
3. Calculate the number of moles of calcium atoms removed:
Avogadro's number (\(N_A\)) is \( 6.022 \times 10^{23} \) atoms/mol.
[tex]\[ \text{Number of moles removed} = \frac{1.2 \times 10^{19} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}} \approx 1.9926934573231485 \times 10^{-5} \, \text{mol} \][/tex]
4. Calculate the remaining number of moles of calcium:
[tex]\[ \text{Remaining moles} = \text{Initial moles} - \text{Moles removed} \][/tex]
[tex]\[ \text{Remaining moles} = 5 \times 10^{-5} \, \text{mol} - 1.9926934573231485 \times 10^{-5} \, \text{mol} \approx 3.0073065426768517 \times 10^{-5} \, \text{mol} \][/tex]
Thus, the number of g-atoms of calcium left is approximately [tex]\( 3.0073065426768517 \times 10^{-5} \)[/tex] g-atoms.
1. Convert the initial mass from milligrams to grams:
[tex]\[ \text{Initial mass in mg} = 2 \, \text{mg} \][/tex]
[tex]\[ \text{Initial mass in grams} = \frac{2 \, \text{mg}}{1000} = 0.002 \, \text{g} \][/tex]
2. Calculate the number of moles of calcium in the initial sample:
Given the atomic mass of calcium (\( \text{Ca} \)) is 40 g/mol,
[tex]\[ \text{Number of moles} = \frac{\text{Initial mass in grams}}{\text{Atomic mass of Ca}} = \frac{0.002 \, \text{g}}{40 \, \text{g/mol}} = 5 \times 10^{-5} \, \text{mol} \][/tex]
3. Calculate the number of moles of calcium atoms removed:
Avogadro's number (\(N_A\)) is \( 6.022 \times 10^{23} \) atoms/mol.
[tex]\[ \text{Number of moles removed} = \frac{1.2 \times 10^{19} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}} \approx 1.9926934573231485 \times 10^{-5} \, \text{mol} \][/tex]
4. Calculate the remaining number of moles of calcium:
[tex]\[ \text{Remaining moles} = \text{Initial moles} - \text{Moles removed} \][/tex]
[tex]\[ \text{Remaining moles} = 5 \times 10^{-5} \, \text{mol} - 1.9926934573231485 \times 10^{-5} \, \text{mol} \approx 3.0073065426768517 \times 10^{-5} \, \text{mol} \][/tex]
Thus, the number of g-atoms of calcium left is approximately [tex]\( 3.0073065426768517 \times 10^{-5} \)[/tex] g-atoms.
