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
[(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.
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
Dm = 242000 J / (3e8)2
= 2.7e-12 kg
= 2.7e-9 g
= 2.7 ng (nanogram)
The fraction of mass lost = 2.7e-9 / 18
= 15 ppb (part per billion)
About 3 ng is insignificant (1.5e-10) in a weight of 18 g.
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?
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
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.