Q1.
Can you calculate how many atoms would be needed to make a sheet of paper that is 0.1 mm thick, like the one in your textbook?
Answer
About 106 atoms — one million atoms stacked one on top of another.
Formula: number of atoms across the thickness = thickness of sheet ÷ diameter of one atom.
Thickness of sheet = 0.1 mm
1 mm = 10–3 m, so 0.1 mm = 0.1 × 10–3 m = 10–4 m
Diameter of one atom ≈ 10–10 m
Number of atoms ≈ (10–4 m) ÷ (10–10 m)
= 10(–4) – (–10)
= 106
= 106 atoms, i.e. about one million (10 lakh) atoms
1 mm = 10–3 m, so 0.1 mm = 0.1 × 10–3 m = 10–4 m
Diameter of one atom ≈ 10–10 m
Number of atoms ≈ (10–4 m) ÷ (10–10 m)
= 10(–4) – (–10)
= 106
= 106 atoms, i.e. about one million (10 lakh) atoms
Notice that the metres cancel, so the answer is a pure number — as it must be, since it is a count.
Why it happens: the calculation works because the answer is a ratio of two lengths. This is also a fair estimate rather than an exact count: atoms in paper are packed in fibres, not in a neat vertical column, and 10–10 m is a typical atomic diameter rather than the value for any one element.
Try This: a human hair is about 0.07 mm = 7 × 10–5 m thick. Number of atoms across it ≈ (7 × 10–5 m) ÷ (10–10 m) = 7 × 105, i.e. about 7 lakh atoms.