To calculate how many thorium atoms would have to be lined up side by side to span 1.80 mm, you can use the following steps:
1. Find the atomic radius of thorium (Th). The atomic radius of thorium is approximately 180 picometers (pm), which is 180 x 10^-12 meters.
2. Convert 1.80 mm to meters. There are 1,000,000 picometers in a millimeter, so 1.80 mm is equivalent to 1.80 x 10^-3 meters.
3. Divide the length you want to span (1.80 x 10^-3 meters) by the atomic radius of thorium (180 x 10^-12 meters):
(1.80 x 10^-3 meters) / (180 x 10^-12 meters) = 10,000,000
So, you would need to line up approximately 10,000,000 thorium atoms side by side to span 1.80 mm.