Page 296 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 19] NUCLEAR REACTIONS 285

These nuclear reactions actually take place in much less than 1 s each, and the number of reactions can
28
exceed 10 within much less than 1 min. Since the energy of each “event” is relatively great, a large amount of
energy is available.
Such nuclear reactions are controllable by keeping the sample size small so that most of the neutrons escape
from the sample instead of causing further reactions. The smallest mass of sample that can cause a sustained
nuclear reaction, called a chain reaction, is called the critical mass. Another way to control the nuclear reaction is
to insert control rods into the nuclear fuel. The rods absorb some of the neutrons and prevent a runaway reaction.
When a positron is emitted from a nucleus, it can combine with an electron to produce energy. Show that
the following equations, when combined, yield exactly the number of electrons required for the product nucleus.
22 22
Na −→ Ne + +1 β
e − + +1 β −→ energy
One of the 11 electrons outside the Na nucleus could be annihilated in the second reaction, leaving 10 electrons
for the Ne nucleus.

19.6. NUCLEAR ENERGY
Nuclear energy in almost inconceivable quantities can be obtained from nuclear fission and fusion reactions
according to Einstein’s famous equation
E = mc 2

The E in this equation is the energy of the process. The m is the mass of the matter that is converted to energy—the
change in rest mass. Note well that it is not the total mass of the reactant nucleus, but only the mass of the matter
that is converted to energy. Sometimes the equation is written as
E = ( m)c 2
8
2
The c in the equation is the velocity of light, 3.00 × 10 m/s. The constant c is so large that conversion of a very
tiny quantity of matter produces a huge quantity of energy.
EXAMPLE 19.10. Calculate the amount of energy produced when 1.00 g of matter is converted to energy. (Note: More
2
than 1.00 g of isotope is used in this reaction.) 1 J = 1kg·m /s 2
2
2
13
10
8
Ans. E = ( m)c = (1.00 × 10 −3 kg)(3.00 × 10 m/s) = 9.00 × 10 J = 9.00 × 10 kJ
Ninety billion kilojoules of energy is produced by the conversion of1gof matter to energy! The tremendous
quantities of energy available in the atomic bomb and the hydrogen bomb stem from the large value of the constant
2
c in Einstein’s equation. Conversion of a tiny portion of matter yields a huge quantity of energy. Nuclear plants also
rely on this type of energy to produce electricity commercially.
Nuclear fusion reactions involve combinations of nuclei. The fusion reaction of the hydrogen bomb involves
2
2
the fusing of deuterium, H, in lithium deuteride, Li H:
1
2 2 3 1
2
1
0
1 H + H −→ He + n
2 2 3 1
1
1 H + H −→ H + H
1
1
6
3
The H produced (along with that produced from the fission of Li) can react further, yielding even greater energy
per event.
3 2 4 1
0
1 H + H −→ He + n
2
1
These fusion processes must be started at extremely high temperatures—on the order of tens of millions of
degrees Celsius—which are achieved on earth by fission reactions. That is, the hydrogen bomb is triggered by an
atomic bomb. Nuclei have to get very close for a fusion reaction to occur, and the strong repulsive force between
two positively charged nuclei tends to keep them apart. Very high temperatures give the nuclei enough kinetic
energy to overcome this repulsion. No such problem exists with fission, since the neutron projectile has no charge