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A nucleus always weighs less than the protons and neutrons that make it up.
This lost mass is the nuclear binding energy: the energy that holds the
nucleus together. (There are a lot of protons jammed in a very small space,
which causes tremendous electrostatic repulsion. Large amounts of energy are
needed to hold a nucleus together.) The binding energy can be computed from the mass-energy
relationship DE = Dmc2. The amount of missing mass is known as the
mass defect
To compute the nuclear binding energy, simply total up the masses of the
protons and neutrons in a nucleus and compare it to the mass of the nucleus.
- Proton mass: 1.00728 amu
- Neutron mass: 1.00867 amu
A table of nuclear masses is in your
book on page 541.
To judge the relative stability of nuclei, binding energy/nucleon is a better
measure than absolute energy since large nuclei always have more binding energy
than smaller. If we look at this measure, hydrogen and helium are very low, iron
is at a maximum, and elements beyond iron drop off.
Example: What is the binding energy for 1 mole of the very stable
5626Fe nucleus?
Solution: An iron-56 nucleus has 26 protons and (56-26) = 30 neutrons.
The total mass is thus
- 26*1.00728 + 30*1.00867 = 56.44938 amu
Looking up the mass of the
iron nucleus, we find that it is 55.92066 amu. This means that the mass defect
is 56.44938 - 55.92066 = 0.52872 amu = 0.52872 g/mole Fe. To convert to energy,
use
- DE = Dmc2
- E = 0.52872 g/mole* 9.00*1010kJ/g
- E = 4.76*1010 kJ/mole
This is a huge amount of energy. |