# What is the volume of an iron atom?

1. Sep 22, 2004

### hytuoc

Plz help ASAP!!!

Iron has a mass of 7.87g/cm^3 of volume, and the mass of an iron atom is 9.27x10^(-26)kg. If the atoms are spherical and tightly packed,
a) a) what is the volume of an iron atom? --> this one I do know how to do it, the answer is 1.18x10^29 m^3
b) what is the distance between the centers of adjacent atoms?
This one, my answer is different than the answer in the book
This was how I did it:
b) [(1.18 x 10^29 m^3) x 3/4] / pi = r^3
r= 3.04 x 10^9 m
=> the distance between the centers of adjacen atoms is 6.08 x 10^9 meters
****but the answer of the book is 0.282 nm
Would someone plz show me how to do part b of the problem? Thanks so much

2. Sep 22, 2004

### christinono

Looks good to me... Are you sure the book contains the right answer?

3. Sep 22, 2004

### Sirus

For a), I assume you meant $1.18\times10^{-29}$. All of the other exponents should also be negative, I believe.

I get $6.05\times10^{-10}$ m for b. I think there's an error in the book. You used the right method.

4. Sep 22, 2004

### christinono

got it!!!

I figured it out!!
Sirus was right, the radius is 1.18X10^-29. The you jst multiply that by 3/4pi and then take the third root. Finally, you multiply it by 2 and get 2.82X10^-10, which is 282nm.

5. Sep 22, 2004

### Sirus

Right, I was putting pi in the numerator in my calculator (hytuoc, I suspect this was also your error). Book was right.