# Hydrogen atom vs hydrogen nucleus. (1 Viewer)

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#### albinoboy

1. The problem statement, all variables and given/known data
A hydrogen atom has a diameter of approximately 1.06x10^-10 m, as defined by the diameter of the spherical electron cloud around the nucleus. The hydrogen nucleus has a diameter of approximately 2.40x10^-15 m.

(a) For a scale model, represent the diameter of the hydrogen atom by the length of an American football field (100 yards = 300 ft) and determine the diameter of the nucleus in millimeters.

(b) The atom is how many times larger in volume than its nucleus?

2. Relevant equations
2.40x10^-15 (1000mm/1m) = 2.40e-12

V=(4/3)*pi*r^3

3. The attempt at a solution
For (a) I got 2.40e-12
It says "Your response differs from the correct answer by orders of magnitude."

For (b) I got 4.42e4
It says "Your response differs from the correct answer by orders of magnitude."

Any help would be greatly appreciated!!

Anyone?

#### collinsmark

Homework Helper
Gold Member
Hello albinoboy,

Just a couple of general pointers:

Don't forget to convert the length of a football field to meters.

How much bigger is the length of a football field than the diameter of a hydrogen atom? So scaling the diameter of the nucleus by the same amount gives us....

You used "2.40x10^-15 (1000mm/1m) = 2.40e-12", but that's just converting the actual diameter of the nucleus from meters to millimeters. I believe the question is asking you to scale up the whole atom to the size of a football field, and then express the scaled-up diameter of the nucleus in millimeters. In other words, "if hydrogen atoms were the size of football fields, how big would hydrogen nuclei be?"

You have the correct relevant equation given for volume. But your answer isn't correct. Showing your work would help get better responses.

#### albinoboy

Hello albinoboy,

Just a couple of general pointers:

Don't forget to convert the length of a football field to meters.

How much bigger is the length of a football field than the diameter of a hydrogen atom? So scaling the diameter of the nucleus by the same amount gives us....

You used "2.40x10^-15 (1000mm/1m) = 2.40e-12", but that's just converting the actual diameter of the nucleus from meters to millimeters. I believe the question is asking you to scale up the whole atom to the size of a football field, and then express the scaled-up diameter of the nucleus in millimeters. In other words, "if hydrogen atoms were the size of football fields, how big would hydrogen nuclei be?"

You have the correct relevant equation given for volume. But your answer isn't correct. Showing your work would help get better responses.
I am unsure if I am following correctly. Do I take 2.40x10^-15 and multiply it by how many meters are in a football field?

#### collinsmark

Homework Helper
Gold Member
I am unsure if I am following correctly. Do I take 2.40x10^-15 and multiply it by how many meters are in a football field?
Not quite. What I'm saying is find,

$$x = \frac{ \mbox{length of a football field, in meters}}{\mbox{diameter of a hydrogen atom, in meters}}$$

Now you can say, Football fields are x times bigger than hydrogen atoms."

Now scale the nucleus diameter by the same amount.

If you're having trouble, think of it this way. You've multiplied the diameter of a hydrogen atom by x to make it as big as a football field. Now multiply the diameter of the nucleus by x to keep it proportional to the size of football field sized atom.

Moving on to part (b). Here you need to find the volume of a hydrogen atom and the volume of a hydrogen nucleus, then divide the two. You can do this directly using your relevant equation. (But you might find it easier to keep things in terms of equations before you divide, because a lot of terms will cancel out and you'll have fewer calculations; although this is not absolutely necessary. You should get the same result either way.)

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