Question

The radius of a lead atom is 175 pm. how many lead atoms would have to be laid side by side to span a distance of 6.11 mm?

Answer 1

The number of atoms needed to be laid side by side to span a distance of 6.11 mm is 17,457,143.

What is Unit conversion?

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

Given that the radius of a lead atom is 175 picometers. Therefore, the radius of the lead atom in mm can be written as,

1 picometer = 10⁻⁹ millimeter

175 picometer = 175×10⁻⁹ millimeter

The radius of the lead atom = 175×10⁻⁹ millimeter

Since the atoms are needed to be arranged side by side, therefore, the diameter of one lead atom will join with the other, thus, the diameter of the lead atom is,

Diameter of lead atom = 2 × 175 × 10⁻⁹ millimeter = 350 ×10⁻⁹ millimeter

Now, let the number of lead atoms be represented by n. Therefore, the number of atoms needed to be laid side by side to span a distance of 6.11 mm is,

6.11 mm = Number of atoms × Diameter of atoms

6.11 mm = n × 350 ×10⁻⁹ mm

Solving for n,

n = 6.11 mm / 350 ×10⁻⁹ mm

n = 17,457,142.86 ≈ 17,457,143

Hence, the number of atoms needed to be laid side by side to span a distance of 6.11 mm is 17,457,143.

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