What is the number density of lead in 1/cm^3?
The Correct Answer and Explanation is:
To calculate the number density of lead (Pb) in units of 1/cm³, we need to know the mass density of lead and its atomic mass. Here’s how we can go through the calculation:
Step 1: Determine the mass density of lead
The mass density of lead (ρ) is given as approximately 11.34 g/cm³.
Step 2: Find the molar mass of lead
The molar mass of lead (Pb) is 207.2 g/mol.
Step 3: Convert mass density to molar density
To find the number of moles per cubic centimeter, we divide the mass density by the molar mass:Molar density=Mass densityMolar mass=11.34 g/cm3207.2 g/mol≈0.0548 mol/cm3\text{Molar density} = \frac{\text{Mass density}}{\text{Molar mass}} = \frac{11.34 \, \text{g/cm}^3}{207.2 \, \text{g/mol}} \approx 0.0548 \, \text{mol/cm}^3Molar density=Molar massMass density=207.2g/mol11.34g/cm3≈0.0548mol/cm3
Step 4: Convert moles to number of atoms
Now, we convert moles to the number of atoms. This requires Avogadro’s number, which is 6.022×10236.022 \times 10^{23}6.022×1023 atoms/mol.Number density=Molar density×Avogadro’s number\text{Number density} = \text{Molar density} \times \text{Avogadro’s number}Number density=Molar density×Avogadro’s numberNumber density=0.0548 mol/cm3×6.022×1023 atoms/mol\text{Number density} = 0.0548 \, \text{mol/cm}^3 \times 6.022 \times 10^{23} \, \text{atoms/mol}Number density=0.0548mol/cm3×6.022×1023atoms/molNumber density≈3.30×1022 atoms/cm3\text{Number density} \approx 3.30 \times 10^{22} \, \text{atoms/cm}^3Number density≈3.30×1022atoms/cm3
Conclusion:
The number density of lead in 1/cm³ is approximately 3.30 × 10²² atoms/cm³. This means that in every cubic centimeter of lead, there are roughly 3.30 × 10²² lead atoms.
