Solving 1st Physics Class: Hydrogen Atom & Nucleus Diameters

[jimen113]

Homework Statement

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.

Homework 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?

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)
answer is: 2.07mm

 

[berkeman]

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...

 

[jimen113]

thanks for your help.
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.

 

[berkeman]

thanks for your help.
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.

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.

 

[jimen113]

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.

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

 

[Redbelly98]

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.