Certainly! Let's solve this step-by-step:
1. Understand the given data:
- Mass of scandium is [tex]\( 708 \)[/tex] micrograms ([tex]\(\mu g\)[/tex]).
- Atomic mass of scandium is [tex]\( 44.9559 \)[/tex] grams per mole (g/mol).
- Avogadro's number is [tex]\( 6.022 \times 10^{23} \)[/tex] atoms per mole.
2. Convert mass from micrograms to grams:
- We know that [tex]\( 1 \)[/tex] microgram ([tex]\(\mu g\)[/tex]) is equal to [tex]\( 1 \times 10^{-6} \)[/tex] grams.
- So, [tex]\( 708 \)[/tex] micrograms can be converted to grams by multiplying by [tex]\( 1 \times 10^{-6} \)[/tex]:
[tex]\[
708 \, \mu g \times 1 \times 10^{-6} = 0.000708 \, \text{grams}
\][/tex]
3. Calculate the number of moles of scandium:
- The number of moles ([tex]\( n \)[/tex]) can be calculated by dividing the mass (in grams) by the atomic mass (in g/mol):
[tex]\[
n = \frac{0.000708 \, \text{grams}}{44.9559 \, \text{g/mol}} \approx 1.5748767125115945 \times 10^{-5} \, \text{moles}
\][/tex]
4. Calculate the number of atoms:
- The number of atoms ([tex]\( N \)[/tex]) is found by multiplying the number of moles by Avogadro's number:
[tex]\[
N = 1.5748767125115945 \times 10^{-5} \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mole} \approx 9.483907562744822 \times 10^{18} \, \text{atoms}
\][/tex]
So, the number of atoms in 708 micrograms of scandium is approximately [tex]\( 9.483907562744822 \times 10^{18} \)[/tex] atoms.
