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Let's break this down and see what we can do with it. First, the probability of transition of an atom from the initial state (m) to final state (n) will depend on what it is that is transitioning, and also on how it's transitioning. Which element - and which isotope - is transitioning? And how it is transitioning? Under what conditions? Radioactive decay? Neutron (or other particle) absorption? With the stating atom and the mode of change, we can determine the probability of transition as was asked. With the first part of the information in hand, we can determine the energy loss in the heavy charged particle emission event. We should also be able to determine the time over which the event takes place, and then discover the rate of energy loss (though it will represent only an average) for said event.

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Q: How can one calculate probability of transition of atom from initial state m to final state n and obtain a formula for rate of energy loss with the emission from the atom of a heavy charged particle?
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