The radius of a gold atom is 144 pm. How many gold atoms would have to be laid side by side to span a distance of 4.97 mm

2.18 × 10⁷ Au atoms

Explanation:

Step 1: Calculate the diameter of a gold atom

The diameter is twice the radius.

d = 2 × r = 2 × 144 pm = 228 pm

Step 2: Convert "d" to meters

We will use the conversion factor 1 m = 10¹² pm.

228 pm × 1 m/10¹² pm = 2.28 × 10⁻¹⁰ m

Step 3: Convert the total distance to be covered (D) to meters

We will use the conversion factor 1 m = 10³ mm.

4.97 mm × 1 m/10³ mm = 4.97 mm × 10⁻³ m

Step 4: Calculate the number of atoms of gold required

We will divide the total distance by the diameter of 1 atom of gold.

D/d = 4.97 mm × 10⁻³ m/2.28 × 10⁻¹⁰ m = 2.18 × 10⁷

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