In this example question, it says the goldfoil Rutherford used in his experiment had a thickness of approximately 6.0×10-3mm. If a single gold atom has a diameter of 2.9×10-8cm, how many atoms thick was Rutherford's foil? All right, so here we need to determine what is our end amount. Here they want us to determine the amount of atoms. So the number of atoms will be our end amount, and our given amount is just the value that possesses only one unit connected to it.
Within this question, we have two values being given here. They're saying that we have 60×10-3mm. And in this other value, it's actually not alone, it's actually a conversion factor. It's telling US1 atom has this value. So the conversion factor is 1 atom is 2.9×10-8cm. Remember we're going to start with our given amount, which is just a value alone that is not connected to another unit. So we have 6.0×10-3mm that is our given amount.
Remember, we use conversion factors to go from our given amount to our end amount and realize here that if I can convert these millimeters into centimeters, they can cancel out with these centimeters and in that way we can isolate atoms at the end. So that is the approach we're going to take. So our first conversion factor is just going to be converting millimeters to meters. Remember the coefficient of one goes on the side with the metric prefix, meaning one milli is 10-3mm.
Can't slop Now I have meters for conversion factor 2. Now I'm going to go from meters to centimeters. One centi is 10-2. Now that I have centimeters, I can now bring in my conversion factor from the question itself, which is conversion factor 3, so 2.9×10-8cm per one atom. So here centimeters cancel out and I'll have atoms at the end. Make sure you put this in parentheses in your calculator, otherwise you make it the incorrect answer.
And remember, we do that every time we have times 1020 power. If you do that correctly, you'll get as your final answer 2.1×104 atoms. So we would have 2×104 atoms in terms of another atoms involved in the thickness of Rutherford's foil.