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Chemistry: Finding the volume of a nucleus & atom, given their respective radii. Help?
By nattymember has saluted, click to view salute photosPremium member Comments: 2042, member since Wed Jul 16, 2003
On Sat Feb 13, 2010 09:47 PM
Locked by natty (69280) on 2010-02-17 16:53:48 I solved my homework.

Okay, here's the problem:

Carbon-12 contains 6 protons and 6 neutrons. The radius of the nucleus is approximately 2.7 fm, and the radius of the atom is approximately 70 pm. Calculate the volume of the nucleus and the volume of the atom. Then find the percentage of the carbon atom's volume that is occupied by the nucleus.

The final answer is supposed to be in meters cubed.
I've tried five times, and am on my last attempt allowed on the online homework. It's due on February 17th at midnight central time.

So here's what I've gathered I must do so far:
I have converted the radius of each thing into meters cubed (because I wasn't sure if you could calculate each with different units), and then plugged into what I found on Google (obviously not totally reliable) the equation for the volume, V= 4/3 times pi times r^3. That should give me my final answer for each one. I've gotten different numbers most times because I'm horrible with conversion factors. The way I type it into the calculator also seems to make a difference, I've gotten different numbers with that as well.

What I tried so far, don't rely on my conversions:
1 pm=10^-12 m,
so 1 pm^3= 10^-36 m^3

so I cubed the given for the nucleus, because that's what I thought I was supposed to do for it to be fm^3. I got 19. 683 fm^3. I tried converting it to meters cubed, and got (rounded to two sig figs) 2.0 x10^-44 m^3.

I cubed the 70 pm to try to get pm^3. I got 34300 pm^3. I tried to convert it to meters cubed. Got (2 sig figs) 3.4 x 10^-31 m^3.

I plugged each in individually, to get basically different answers a bunch of times. I don't really think I even went about this the right way, but hopefully someone can point me in the right direction.

2 Replies to Chemistry: Finding the volume of a nucleus & atom, given their respective radii. Help?

re: Chemistry: Finding the volume of a nucleus & atom, given their respective radii. Help?
By webstArmember has saluted, click to view salute photos Comments: 3639, member since Wed Jan 15, 2003
On Sun Feb 14, 2010 12:00 PM
Edited by webstAr (54294) on 2010-02-14 12:00:34
I won't get into all of your numbers right now, but I believe that your mistake is trying to get your values into meters cubed beforehand - that isn't necessary and is giving you the wrong answer. Actually, it's giving you an answer where the units would be m^6.

m^3 happens through the equation 4/3pi*r^3. Plug your initial values for the radii into that equation.
re: Chemistry: Finding the volume of a nucleus & atom, given their respective radii. Help?
By nattymember has saluted, click to view salute photosPremium member Comments: 2042, member since Wed Jul 16, 2003
On Wed Feb 17, 2010 04:53 PM
Thank you. I did the problem correctly except that I was not supposed to cube the measurements before the problem.

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