Question

I feel really dumb because I cant figuer out this simple algebra I problem...

84. The diameter of a copper (Cu) atom is roughly 1.3 x 10^-12 m. How mnay times can you divide devenly a piece of 10-cm copper wire until it is reduced to two separate copper atoms? (Assume there are appropriate tools fo rthis procedure and that copper atoms are lined up in a stragiht line, in contact with each other. Round off your answer to an integer.)

The back of the book says 36 times which I don't see how...

Answer 1

your are cutting the wire in half, so you are solving

1.3x10^-12 = 1x10^-2 (1/2)^n , where n is the number of times.
1.3x10^-11 = (.5)^n
log[1.3x10^-11] = log(.5^n)
n = log[1.3x10^-11] / log .5
n = 36.16
or
n = 36

Answer 2

my first line has a typo, should have been
1.3x10^-12 = 1x10^-1 (1/2)^n , where n is the number of times.

Answer 3

I agree that 36 times seems fishy to me; however, the answer is correct. The secret word may be "evenly".
How many atoms do we have lined up in 0.1 meter?
1.3 x 10^-12 m/atom x # atoms = 0.1m
Solve for # atoms and I get something like 7.69 x 10^10 but you need to verify that.
Now the first slice cuts it in half (and you now have 3.8 x 10^10 pieces in the half you will cut next.
The second slice leaves 1.9 x 10^10 atoms in your hand.
The third slice leaves 9.6 x 10^9 in your hand.
Continue cutting until you get to 1 piece in your hand.
If I do that 36 times, I'm left with 1.11 pieces in my hand. I don't know what we do with the 0.11 piece of an atom (perhaps those end up as electrons, protons, and neutrons). :-)

Answer 4

Reiny's answer is more esoteric than mine. It's more sophisticated because he used math to solve the problem and I just iterated it. It's easier to punch my divide button 36 times than it is to burn my brain trying to deduce the math.