Expert: Philip Stahl - 11/23/2009

Question
Thanks, Phillip, for that detailed answer! I will peruse it in depth, when I get more time, later today. Until then, what about the possibility of the expansion of molecules - the 'space' between atoms? Is it possible that molecules are expanding? Thanks, Bruce

Answer
Hello again,

No, there is no chance molecules are expanding either. Again, if it were the case, then molecular spectroscopy - especially as applied to emission and other nebulae in space, would reveal it. But there are no abnormal signals, and the molecular spectra haven't altered - which would imply that the constants governing them haven't either.

For example, a typical diatomic molecule may execute vibration about an equilibrium point, and for which small vibrations of the molecule will occur at a frequency:

f_c = (1/2pi) [C/m]^1/2

where C is the "force constant": C =  [d/dr{dP(r)/dr}]_r=r_o

where r_o is the equilibrium position.

Note the change of P(r) - the potential energy of the molecule, is with respect to r - the RADIUS of the molecule.

It may be shown that the energies associated with such an oscillating molecule will assume values of energy:

E_f = (f + 1/2)h-bar [C/m]^1/2


of  

E_f = (f + 1/2) hf_c

where h is again Planck's constant. and f_c is as defined earlier.

Now, what if we were to allow the radius of the molecule to expand, meaning (r - r_o) would get ever larger and the vibrations about the equilibrium position (r_o) would take longer and longer?

I think you can see that the potential energy "well" (which sustains the molecule as a unit) would soon be breached and the atoms comprising it would be detached. There is only so much energy that can support it.

If one were to command extra energy to sustain the diatomic unit (prevent the breach from occurring) then the energy E_f would have to increase correspondingly - meaning h would have to alter (get much larger).

But, when we observe vibrational spectra of molecules, we continue to observe defined and quantized levels viz.

---E3 = 7hf_c/ 2 ---f = 3

---E2 = 5hf_c/ 2 ---f = 2

---E1 = 3hf_c/ 2 ---f = 1

---E_o = hf_c/2 -----f = 0 (zero point energy)


These levels observed in molecular (vibrational) spectra clearly show the (energy) spacings are normal and conform to the energies and frequencies computed for the already existing and defined values of r_o, (r - r_o) for given molecules.

Thus, the results of the spectral analysis-features show NO constant expansion of the molecule itself!

To put it another way, we don't detect or observe the radical change in the vibrational spectra that would support any such "molecular expansion" analogous to a cosmic expansion.