Iron has a mass of 7.87 g per cubic centimeter of volume, and the mass of an iron atom is 9.27 * 10^-26 kg. If you simplify and treat each atom as a cube, (a) what is the average volume (in cubic meters) required for each iron atom and (b) what is the distance (in meters) between the centers of adjacent atoms?
The Attempt at a Solution
I managed to come up with (a) on my own, which was:
1.17789 * 10^-29 m
However, for (b), I'm confused as to exactly how it got the answer:
0.282 nm = 0.282 * 10^-9 m
At first I treated each atom as a cube and got some answers that were way off.. I took the hint and it mentioned that you should treat each atom as a sphere (WTF? It says cube in the problem, but whatever), so using the formula for that, I got
V = (4/3)*pi*r^3 = 1.17789 * 10^-29 m
Solving for r^3 I had
r^3 = 0.281200696 * 10^-29
Now solving for r in this case was problematic because depending on where you place the decimal point, you get a wildly different answer for the cubed root of this figure, in your scientific calculator. But the figure looks similar to the actual answer, except that the magnitude was cube-rooted or something..
I'm still pretty stumped... Could someone explain what I'm doing wrong?
UPDATE: Never mind, I found out that 1) the problem was stated correctly, the hint was a red herring, and 2) I can use Mathematica to find the proper cube-root of numbers in scientific notation.