Intro physics proportion question

[dylanhouse]

Homework Statement

The radius of a proton is roughly 10^-15m, while the radius of a hydrogen atom is about 0.5x10^-10m. If we were to enlarge both proportionally until the proton was as large as a marble, about how large would the atom be?

Homework Equations

The Attempt at a Solution

I calculated an answer of 300m, but this doesn't seem correct for the size of a Hydrogen atom. I simply took the radius of a marble to be approximately 0.6cm, found the proton had to increase by 6x10^12 to become the size of the marble and multiplied this increase factor by the radius of the hydrogen atom and got 300 :$

 

[gneill]

The proportion looks okay. The straightforward approach is to set up the ratios as an equation.

$$\frac{r_{hydrogen}}{r_{proton}} = \frac{r_x}{r_{marble}}$$

 

[dylanhouse]

What is rx? I'd have (0.5x10^-10)/(10^-15)=rx/x? Assume the marble radius is x..

 

[gneill]

$r_x$ is the unknown radius of the "inflated" atom.

 

[dylanhouse]

I guess my question is how would I use that ratio to show that the atom is always 50,000 times larger than proton?

 

[gneill]

I guess my question is how would I use that ratio to show that the atom is always 50,000 times larger than proton?

The ratio is a given. You have the radius of the proton, and the radius of the hydrogen atom. The rest is just proportional scaling (or comparison) of sizes.