Intro physics proportion question

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Homework Help Overview

The discussion revolves around a proportionality question in introductory physics, specifically comparing the sizes of a proton and a hydrogen atom when both are enlarged proportionally. The original poster presents a calculation involving the radii of both particles and seeks clarification on the resulting size of the hydrogen atom when the proton is scaled up to the size of a marble.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to calculate the enlarged size of a hydrogen atom based on the proportional increase of a proton's size. Some participants suggest setting up a ratio to find the unknown size of the hydrogen atom, while others question the interpretation of the ratio and how it relates to the known size difference between the two particles.

Discussion Status

Participants are actively discussing the proportional relationship between the sizes of the proton and hydrogen atom. There is an ongoing exploration of how to set up the equations correctly, and some guidance has been offered regarding the use of ratios. However, there is no explicit consensus on the correct approach or final answer yet.

Contextual Notes

Participants are working under the assumption that the scaling factor between the proton and hydrogen atom is consistent, with the known ratio of their sizes being approximately 50,000 times. There is a focus on ensuring that the calculations reflect this proportionality accurately.

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

$$\frac{r_{hydrogen}}{r_{proton}} = \frac{r_x}{r_{marble}}$$
 
What is rx? I'd have (0.5x10^-10)/(10^-15)=rx/x? Assume the marble radius is x..
 
##r_x## is the unknown radius of the "inflated" atom.
 
I guess my question is how would I use that ratio to show that the atom is always 50,000 times larger than proton?
 
dylanhouse said:
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.
 

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