Uranium238 vs U235, which are true?

[Kibbel]

Homework Statement

Uranium-238 (U238) has three more neutrons than uranium-235 (U235). Compared to the speed of sound in a bar of U235, is the speed of sound in a bar of U238 higher, lower, or the same? There are several factors that play a role.

(a) Chemically, the atoms of these two isotopes behave in essentially identical ways, since the number of protons (92) is identical and the clouds of 92 electrons are nearly identical. The interatomic distance, and the effective "stiffness" of the interatomic bond, both depend on the chemical properties of the atoms. Therefore, which of the following statements are true?

1. The interatomic distance is the same for the two isotopes, because it depends on the size of the electron cloud, not the nuclear mass.

2. An atom with more mass in the nucleus is bigger, so the distance between neighboring atoms is larger.

3.The effective stiffness of the interatomic "spring" is the same in the two isotopes, since this "spring" is a model for the interactions of the outer electrons, which are the same for different isotopes of the same atom.

4.The effective stiffness of the interatomic "spring" is greater for U238 because the mass is greater.

Homework Equations

none

The Attempt at a Solution

I thought it was that the interatomic distance in between the two are the same, (#1). I am not sure whether it has to do with the electron, but I was pretty sure that it doesn't have to do with the mass. this is why i didn't check 2 or 4 either. Because I know two things can have the same mass, but they don't neccissarily have to be bigger, because the density might be different. Or maybe the entire thing is different on the microscopic level?

can someone help me out?

 

[Andrew Mason]

Think of the atoms comprising the metal as little balls connected to other little balls with springs. What two parameters determine the speed at which a vibration travels through this mass/spring web?

As is pointed out, in the case of U₂₃₅ and U₂₃₈ there is no difference in "spring" constant, only a difference of mass.

AM