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Nuclear energies

The mass (m) of a particle moving with a velocity v is larger than its rest mass mo, according to Einstein's theory of relativity
m = mo
----------------
[(1 - (v/c)2]1/2

Einstein further showed that the increase in kinetic energy DE is equal to Dm c2.

DE = Dm c2 Where c is the velocity of light. The equation shows that energy and mass convert into each other, and both must be taken considered when applyint the principle of conservation of energy.

Example 1

One mole of hydrogen and half a mole of oxygen react to produce 18.0 g of water vapor and 242 kJ of heat. What is the mass equivalent of this energy?

Solution

Dm = 242000 J / (3e8)2
    = 2.7e-12 kg
    = 2.7e-9 g
    = 2.7 ng (nanogram)

Discussion

The fraction of mass lost = 2.7e-9 / 18
    = 1.5e-10
    = 15 ppb (part per billion)

About 3 ng is insignificant (1.5e-10) in a weight of 18 g.

Example 2

When a deuterium atom and a tritium atom fuse to give a helium atom plus a neutron, 2.82e-12 J is released. The total (rest) mass of a deuterium and tritium is 8.35272e-24 g. What is the total (rest) mass of the helium and the neutron after the fusion reaction?

Solution

First of all, the mass equivalence of the energy released is

Dm = (2.82e-12 J) / (3e8)2
    = 3.133e-29 kg
    = 3.133e-26 g

Total mass of product = (8.35272e-24 - 3.133e-26) g
    = 8.35269e-24 g

Discussion

The fraction of mass lost = 3.133e-26/8.35272e-24
    = 0.38 %

In terms of round figures, about 4 thousandth of the mass is lost.

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E-mail: cchieh@uwaterloo.ca