ratio of atom

[chiddler]

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The size of a U nucleus is about 10 ^-14 m and the size of the U atom is approximately 10^-10 m. Therefore, if the nucleus were the size of a marble, the atom would be the size of:

A. a car
B. an average house
C. a sports stadium
D. the moon

Answer: C.

So i'd like to make sure that this question is indeed ******ed. Or perhaps i'm missing something important.

My thought was "could I put 10,000 marbles in my car? yeah, maybe." Turns out that I can't lol.

 

[Buttafuoco]

i think the key here is get the ratio (the atom is 10^4 times bigger than the diameter or radius of the nucleus) then multiply it by the diameter of a marble. 1 cm is a pretty decent guess and since 1cm is 10^-2m, multiply that by 10^4 and you get 100m. That's around the length of a football field, which definitely takes cars and the moon out of the equation. Remember that you are dealing with meters therefore diameter and not area or volume.

It's actually a kind of crappy question because I don't think the answer is super clear between house and stadium, but something in the neighborhood if 100m is closer to a stadium than most houses.

 

[chiddler]

but that's just looking at it in two dimensions. if we look at 1 cm^3, 100^2 = 10,000 marbles can fit inside one square meter, no?

 

[Buttafuoco]

They are telling you here that it's 10,000x "bigger" in terms of diameter. Since volume = 4/3*pi*r^3, that means that the atom is also 10^12 more voluminous than the nucleus. Or 10^8 times greater in area.

 

[chiddler]

that sounds right.

thanks.

 

[Class1P]

It's a bad question, they mean to tell you that it is the diameter. So if you line them up end to end it's about 10,000 times the length of a marble.

 

[pfaction]

I love TPR sometimes, their answers are like...what.