To determine the number of barium atoms in a [tex]\(9.8 \times 10^{-21}\)[/tex] gram sample, we can follow these steps:
### Step 1: Determine the number of moles of barium in the sample.
First, we need to know the molar mass of barium, which is 137.327 grams per mole.
We can use the formula:
[tex]\[ \text{moles of barium} = \frac{\text{sample mass}}{\text{molar mass of barium}} \][/tex]
Given that the sample mass is [tex]\(9.8 \times 10^{-21}\)[/tex] grams and the molar mass of barium is 137.327 grams per mole:
[tex]\[ \text{moles of barium} = \frac{9.8 \times 10^{-21} \text{ grams}}{137.327 \text{ grams per mole}} \][/tex]
This calculation yields:
[tex]\[ \text{moles of barium} \approx 7.136251429070758 \times 10^{-23} \][/tex]
### Step 2: Determine the number of barium atoms from the moles of barium.
Next, we use Avogadro's number, which is [tex]\(6.022 \times 10^{23}\)[/tex] atoms per mole, to convert moles of barium to the number of atoms.
Using the formula:
[tex]\[ \text{number of atoms} = \text{moles of barium} \times \text{Avogadro's number} \][/tex]
We have:
[tex]\[ \text{number of atoms} = 7.136251429070758 \times 10^{-23} \text{ moles} \times 6.022 \times 10^{23} \text{ atoms per mole} \][/tex]
This calculation yields:
[tex]\[ \text{number of atoms} \approx 42.97 \][/tex]
### Step 3: Round the answer to two significant figures.
Since the problem specifies that the answer should have two significant figures, we round 42.97 to two significant figures:
[tex]\[ \text{number of atoms} \approx 43 \][/tex]
### Final Answer
Thus, the number of barium atoms in a [tex]\(9.8 \times 10^{-21}\)[/tex] gram sample is approximately [tex]\(43\)[/tex].
