What is the volume of an iron atom?

[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 please show me how to do part b of the problem? Thanks so much

 

[christinono]

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

 

[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.

 

[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.

 

[Sirus]

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