# Isotopes and Speed Question

1. Feb 14, 2008

### astros10

If you have two isotopes, would the speed of sound through the atom be larger in the heavier isotope or the lighter isotope, or would they be equal, and why?

2. Feb 15, 2008

### rohanprabhu

Isotopes have nearly the same atomic radii i.e. they take the same amount of space. But, their masses are different. So, basically a heavier isotope means a greater density.

For almost all states of matter, the speed of sound through a given material is inversely proportional to the square root of it's density.

So, the speed of sound must be higher in the lighter isotope.

But, it also depends on the 'Bulk modulus' or the 'Young's modulus' for that material. And since those parameters are governed by electrostatic forces and hence not really controlled by the nuetrons, i guess those values should more or less be same for all isotopes.

3. Feb 15, 2008

### ZapperZ

Staff Emeritus
Since "speed of sound" depends on how well the atoms of the material vibrates, then you should think about an analogous situation. Look at a mass-spring system. What will change if you change the mass? Now imagine a lattice of all of these atoms all connected to each other with springs. If the mass of the atoms change, how will the vibration at one end transfers to the other?

Zz.