Untitled - Kelly Walsh High School

298 CHEMISTRY FOR THE UTTERLY CONFUSED
Substituting this rate constant into equation (1):
ln (65/100) (1.21 10 4 y 1 ) t
0.4308 (1.21 10 4 y 1 ) t
t 3560.33 3.6 × 10 3 y
20-4 Mass/Energy Conversions
Don’t Forget!
Whenever a nuclear decay or reaction takes place, it releases energy. This
energy may be in the form of heat and light, gamma radiation, or kinetic energy
of the expelled particle and recoil of the remaining particle. This energy results
from the conversion of a very small amount of matter into energy.
In a nuclear reaction, there is no conservation of matter as in ordinary chemical
reactions.
The amount of energy that is produced can be calculated by using Einstein’s
relationship, E mc 2 , where E is the energy produced, m is the mass converted
into energy (the mass defect) and c is the speed of light. The amount of matter
converted into energy is normally very small, but when we multiply it by the
speed of light (a very large number) squared, the amount of energy produced is
very large.
When 1 mol of U-238 decays to Th-234, 5 10 6 kg of matter is converted to
energy (the mass defect). Calculate the amount of energy released.
Solution:
E mc 2
E (5 10 6 kg) (3.00 10 8 m/s) 2
E 4.5 10 11 kgm 2 /s 2 5 10 11 kgm 2 /s 2 5 10 11 J