GRE Question (Atomic Physics)

[HungryChemist]

Homework Statement

The Ratio of the nuclear radius to the atomic radius of an element near the middle of the periodic table is most nearly
a) 10^-2
b) 10^-5
c) 10^-8
d) 10^-11
e) 10^-14

Homework Equations

The Attempt at a Solution

I am completely lost. Can someone tell me what they mean by radius of nucleus? My mere guess is that it could be approximated to be equal to the radius of hydrogen. Also, how can one compute the atomic radius? If anyone here knows 'back of the envelope' approach to this problem, please help!

 

[Dick]

It can be approximated by an appropriate multiple of the radius of the proton. The usual approximation is to assume the nucleus packs together like atoms in a liquid drop. It's hard to pick among your multiple choices without any units.

 

[malawi_glenn]

units is not needed, he needs the ratio.

The size of an atom is (if we have classical approach) a couple of Å, and the atomic nucleus a couple of fermi meters.

 

[Dick]

units is not needed, he needs the ratio.

The size of an atom is (if we have classical approach) a couple of Å, and the atomic nucleus a couple of fermi meters.

Very true. Sorry. So you need to think of how the electron shell scales with Z vs how the nuclear radius scales with Z.

 

[HungryChemist]

Very true. Sorry. So you need to think of how the electron shell scales with Z vs how the nuclear radius scales with Z.

How do I do just that?

 

[malawi_glenn]

But this is simple

atomic radius 10^-10 m

Nuclear radius 10^-15m

make a guess

or just look up "atomic radius" and "Nuclei radius" for example Copper and confirm.

 

[Meir Achuz]

Very true. Sorry. So you need to think of how the electron shell scales with Z vs how the nuclear radius scales with Z.

Only the inner electrons scale with Z.
The outer electrons for any atom are about 1/2 Angstrom from the nucleus.
If you take the GRE, you should know that good approximation for the nuclear radius is
R=1.2 A^(1/3). fm.

 

[Gokul43201]

Only the inner electrons scale with Z.
The outer electrons for any atom are about 1/2 Angstrom from the nucleus.

This is way off. For starters, only 4 or 5 elements come close to a 1/2 Angstrom radius: H, He, Na, O and F, the 5 smallest atoms. There are less than 15 elements with valence radii less than 1 Angstrom. Furthermore, even among atoms with the same number of occupied shells, the size of the atom can vary by more than a factor of two: K is about 2.5A while Kr is only about 0.9A, and they both lie in the same period.

Really, there is nothing more to this question than what is posted by mw in post #6.