Question

You buy a cloth that is embedded with silver atoms (supposedly good for cleaning). The cloth is 12" x 10.0 cm x 25 mm, and the company says that there are 3.5 x 1026 silver atoms per nL. You use it to wash dishes. Everytime you wash 1 dish, you lose 20 atoms of silver. In a day, you wash 20 dishes. How many days will your cloth last? (Let’s say it stops working as soon as you lose the last atom.)

Answer 1

12 inches = 304.8 mm

10 cm = 100 mm

Volume of the Cloth = 304.8 mm * 100 mm * 25 mm = 762000 mm^3

Volume in Liters = 762000 * 10^(-6) L = 0.762 L

Number of silver atoms = 3.5 * 10^(26) * 10^(9) * 0.762 = 2.667 * 10^(35) atoms

Number of silver atoms lost in a day = 20 * 20 = 400 silver atoms

Number od days the cloth will last = (2.667 * 10^(35))/(400) = 2.667 * 2.5 * 10^(32) = 6.6675 * 10^(32) days