1. Aug 29, 2008

jimen113

1. The problem statement, all variables and given/known data
A hydrogen atom has a diamter of approximately 1.06x10^-10m, as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has a diameter of approximately 2.4x10^-15m.

2. Relevant equations
(a) for a scale model, represent the diameter of the hydrogen atom by the playing length of an American football field (100yards=300ft) and determine the diameter of the nucleus in millimeters
(b) the atom is how many times larger in volume than it nucleus?

3. The attempt at a solution:
I don't know how to utilize the (100yards=300ft) to find the diameter of the nucleus
I tried converting 2.4x10^-15m into ft and used (100yards=300ft) to find the diameter in mm but the answer is wrong. I got (2.40x10^-12mm)

2. Aug 29, 2008

Staff: Mentor

It appears to be a straight ratio problem. What is the ratio of the nucleus to the atom in this question? It is a number much less than 1. What is it?

Then take that same ratio, based on the American football field's size. If they want the answer in mm (MKS units), you need to convert the 100 yard length into meters. Do you know how to do that? You should be able to find a standard conversion table or calculator on the web...

3. Aug 29, 2008

jimen113

1. I think the ratio of the nucleus to the atom is: (1.06x10^-10/2.4x10^-15)= 4.417X10^-26??
2. I will use the conversion factor (1yd=0.914 4m) once I get the ratio figured out.

4. Aug 29, 2008

Staff: Mentor

No, your ratio in -1- is not correct. Did you use a calculator? The ratio will have an exponent that is the difference of the two exponents in the numerator and denominator, not the sum.

5. Aug 29, 2008

jimen113

Looks like I'm an idiot, sorry
yes, I did use a calculator. Maybe the way I plugged in the #'s into the calculator was what went wrong. I tried using parantheses and I got this #: 44166.667, and you said that
"It is a number much less than 1. What is it?"
so the above answer is >1

6. Aug 29, 2008

Redbelly98

Staff Emeritus
That's okay. You got the ratio of the atom-to-nucleus, when berkeman said to find the nucleus-to-atom ratio. So the number is 44167 or 1/44167, it doesn't matter which as long as you keep in mind the nucleus is smaller than the atom.

Now you just need to convert the football field into m or mm. And since the field is modeling the atom, use the ratio number to figure out the model nucleus size.