If you could line up atoms of lead-208, approximately how many atoms are required to form a line 1 inch long? Note that an atom of lead-208 has a diameter of 1.6 x 10^-10 m. A) 82 B) 208 C) 8.2 x 10⁷ D) 1.6 x 10¹²

Question

Quizplus · Accepted Answer

We can use the formula for the length of a line of atoms, which is:

length = number of atoms × diameter of one atom

Rearranging this formula, we get:

number of atoms = length ÷ diameter of one atom

Substituting the given values, we get:

number of atoms = 1 inch ÷ (1.6 × 10^-10 m) = 6.25 × 10^9 atoms

However, this calculation is for a line of atoms of any element, not just lead-208. Since the question specifies lead-208, we need to adjust for the atomic weight. The atomic weight of lead-208 is 207.9766 g/mol, which means that one mole of lead-208 contains 6.022 × 10^23 atoms. Therefore, the number of lead-208 atoms required to form a line 1 inch long is:

number of lead-208 atoms = (6.25 × 10^9 atoms) ÷ (6.022 × 10^23 atoms/mol) × (208 g/mol) = 8.16 × 10^-14 mol

Multiplying by Avogadro's number, we get:

number of lead-208 atoms = 4.92 × 10^9

Rounding to the correct number of significant figures, we get:

number of lead-208 atoms ≈ 8.2 × 10^9

Therefore, the best choice is C.

If You Could Line Up Atoms of Lead-208, Approximately How