Question

A typical atom has a diameter of about 4.56 x10 -10 m
a) What is the diameter in Inches and µm?
b) Approximately how many atoms are there along a 1.0 cm line?

Answer 1

a) 1 inch = 2.54 cm, therefore $1 m = \dfrac{100\,cm}{2.54 cm/inch}.$ Next,

$4.56 \times 10^{-10} m = 4.56 \times 10^{-10} \times \dfrac{100\,cm}{2.54 cm/inch} = 1.80\times 10^{-8}\, inch.$

1 $\mu m = 10^{-6}m,$ so $\;\; 4.56 \times 10^{-10} m = 4.56\times 10^{-4} \times 10^{-6}\, m = 4.56\times 10^{-4} \,\mu m.$

b) To calculate the number of atoms we should divide 1.0 cm by the diameter of a single atom, so we get

$N=\dfrac{1.0\,cm}{4.56\times10^{-10}\,m} = \dfrac{0.010\,m}{4.56\times10^{-10}\,m} = 21929824 \approx 2.2\cdot10^7.$

The number is approximately 22 mln.