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Almost everyone has heard of Einstein's famous equation E = mc2.
Fewer people understand what it means: that energy (E) and mass (m) can be
interconverted. During a nuclear reaction, we can compute the energy change by
weighing the products and the reactants and using the relation
- DE = Dmc2
to compute the change in energy.
(The same is true for chemical reactions, but the change in mass is so small
that it's impossible to measure.) A table of nuclear masses is available on page
504 of your book. Since c, the speed of light is in somewhat difficult to use
units, we can convert it to a more useful set of units and get another form of
the above equation is
- DE = Dm*9.00*1010kJ/g
Example: What is the change in energy when 1 mole of the radioactive
isotope 3H undergoes beta decay to
form 3He?
Solution: The beta decay of tritium is
- 31H -> 0-1e +
32He
Looking up the masses, we find
- 31H: 3.01550 amu
- 32He: 3.01493 amu
- e-: 0.00055 amu
The change in mass is product mass -
reactant mass, so (3.01493 + 0.00055) - 3.01550 = -0.00002 amu = -0.00002
g/mole. Plug this back into the mass-energy relationship. We've got 1 mole, so
the mass change is -0.00002 g:
- DE = Dm*9.00*1010kJ/g
- DE = -0.00002 g*9.00*1010kJ/g
- DE = -2*106 kJ
This is a
very large amount of energy compared to chemical reactions which have an energy
change on the order of 10s of kJ/gram. |