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September 10, 2007
Counting Tiny Things
If you need to count a great many identical things, it’s usually easiest to count a subset of
them and measure some bulk property of that subset of them, then measure the bulk
property for the whole quantity.
We can use the factorlabel
method to do this. 200 1$ bills make a stack approx. 1 in
high. Id we have a stack 6 inches high we can calculate the approx. value.
(200 bills/inch stack) x 6 inch stack = 1200 bills
Another example:
I’ve got jar with about 3.5 lbs of quarters in it. I weighed 20 quarters, and they weighed
2.5 oz. How much money is in my jar?
We start with 3.5 lbs of quarters. We multiply y the conversion factor from pounds to
ounces. We cancel the pounds. We multiply by a conversion factor from ounces to
number of quarters. The ounces cancel. We multiply by the quarter to dollar conversion
factor. The quarters cancel, giving us an answer.
Counting Atoms
Same thing. only now doing something chemical.
How many atoms are there in a3.54 g of Nickel. Nickel has an atomic mass of 58.6934
amu and 1 amu = 1.6605 x 10^24 g.
We start with 2.54 grams of Nickel. We multiply by the conversion factor from grams to
amu. We cancel the grams. We divide tbyt eh atomic mass of Nickel.
3.54 g x (1 amu/1.66 x 10^24) x (1 atom/58.7 amu) = 2.62 x 10^22
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