[maakii]

Hi, I recently came across the inversion of ammonia, and was quite puzzled over the term "tunneling frequency"..

I think that it is supposed to be the frequency which it absorbs so as to have enough energy for the nitrogen atom to invert, is that right? It would then follow the formula E=hv, and we could then find the energy difference between the transition state and the lowest energy state.

Someone told me that it was the amount of times it inverted a second, and so I am now not sure.
He said that if we replaced the hydrogen atoms in NH₃ with deuterium atoms, this would make it heavier and thus invert less, that is, tunneling frequency decreases.

However, from what I have learnt, making it heavier will increase the energy between transition state and the lowest energy state (ie the barrier), thus, em waves would have to have a higher frequency to provide enough energy for the invertion.

So, who is correct?

[FeLiXe]

tunneling is a quantum mechanical phenomenon that let's a particle cross an energy barrier even if its energy is lower (it digs a tunnel through the barrier). besides the width and height of the barrier, the mass of the particle is important. generally quantum effects increase if the mass is lower. this is also true for tunneling. that's why with increasing mass it will tunnel less likely. it tunnels less often (the tunneling frequency decreases)

that's how I understand it anyway

[maakii]

Hi thanks for the reply! But from what I have recently found out, when the energy barrier is increased, lets say by having a heavier molecule, the tunneling splitting of energy levels decreases (the energy difference between n=1 and n=2), and so the tunneling frequency (frequency of the em radiation corresponding to the energy difference) decreases.

But if I do it this way, does it mean that tunneling frequency does not actually refer to the rate of tunneling? (although it may be a useful "concept"?)

[FeLiXe]

an important thing is that the splitting of energy levels decreases just by increasing the mass, without changing the energy barrier. another effect is that the probability to find a particle inside the barrier decreases with increasing mass and with V-E (potential energy barrier - energy of the particle). with more energy levels the tunneling probabilty decreases for the ground state because V-E increases.

I have this little tunnenling program. you can look at it if you have visual basic or if you download the VB-dll. it shows a potential well with an infinite and a finite barrier. that is kind of one half of your problem

I don't really know what "tunneling frequency" refers to, but in general excitation frequencies seem to be related to something actually oscillating. you can only produce an electromagnetic wave of a frequency if something oscillates with that frequency. The tunneling frequency may be both: the rate and the difference between the energy levels

[maakii]

I think I understand it now, thank you