Calculating energies for a nuclear reaction?

[tomsthename]

So I was doing physics homework today, and wound up spending a couple hours on wikipedia, browsing through topics far out of my league- particularly nuclear physics. I'm left with an aching question that I hope someone here can help me out with.

In a nuclear reaction that requires a certain energy to occur, how do you determine what this energy is? Can it be done mathematically or is it purely experimental? For example, in this reaction (don't worry I'm not a wannabe alchemist... just an example that stuck out in my mind)
Mercury 198 + 6.8MeV gamma ray => neutron + Mercury 197

How can you tell that the gamma ray energy needs to be 6.8MeV?

Thanks in advance. Hope to stick around here.

 

[mathman]

So I was doing physics homework today, and wound up spending a couple hours on wikipedia, browsing through topics far out of my league- particularly nuclear physics. I'm left with an aching question that I hope someone here can help me out with.

In a nuclear reaction that requires a certain energy to occur, how do you determine what this energy is? Can it be done mathematically or is it purely experimental? For example, in this reaction (don't worry I'm not a wannabe alchemist... just an example that stuck out in my mind)
Mercury 198 + 6.8MeV gamma ray => neutron + Mercury 197

How can you tell that the gamma ray energy needs to be 6.8MeV?

Thanks in advance. Hope to stick around here.

Start with E=mc². The masses of Hg198, Hg197, and neutron are all known. The mass difference (Hg197 + n - Hg198) converted into energy gives the energy of the gamma ray.

 

[jtbell]

If your textbook doesn't provide a table of isotope masses, try Google:

http://www.google.com/search?q=table+of+isotope+masses