NUCLEAR ENERGY

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

The c in the equation is the velocity of light, 3.00 × 10 8 m/s. The constant c 2 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 = 1 kg·m 2 /s

Ans.

9.00 × 10 13 J = 9.00 × 10 10 kJ Ninety billion kilojoules of energy is produced by the conversion of 1 g of matter to energy! The tremendous

E = ( m)c 2 = (

1.00 × 10 − 3 kg)(3.00 × 10 8 m/s) 2 =

quantities of energy available in the atomic bomb and the hydrogen bomb stem from the large value of the constant c 2 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

the fusing of deuterium, 2 H, in lithium deuteride, Li 1 2 H:

1 H+ 2 1 H −→ 3 2 He + 1 0 n

1 H+ 2 1 H −→ 3 1 H+ 1 1 H The 3 H produced (along with that produced from the fission of 6 Li) can react further, yielding even greater energy per event.

1 H+ 1 H −→ 2 He + 0 n

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

NUCLEAR REACTIONS

[ CHAP. 19

and can easily get close to the nuclear target. (A report was made in 1989 of a “cold fusion” reaction—a fusion reaction at ordinary temperatures with relatively little energy input—but that report has not yet been confirmed.) The stars get their energy from fusion reactions at extremely high temperatures.

The mass of matter at rest is referred to as its rest mass.When matter is put into motion, its mass increases corresponding to its increased energy. The extra mass is given by

E = mc 2

When a nuclear event takes place, some rest mass is converted to extra mass of the product particles because of their high speed or to the mass of photons of light. While the total mass is conserved in the process, some rest mass (i.e., some matter) is converted to energy.

Nuclear binding energy is the energy equivalent (in E = mc 2 ) of the difference between the mass of the nucleus of an atom and the sum of the masses of its uncombined protons and neutrons. For example, the mass of a

2 He nucleus is 4.0015 amu. The mass of a free proton is 1.00728 amu, and that of a free neutron is 1.00866 amu. The free particles exceed the nucleus in mass by

2(1.00728 amu) + 2(1.00866 amu) − 4.0015 amu = 0.0304 amu

This mass has an energy equivalent of 4.54 × 10 − 12 J for each He nucleus. You would have to put in that much energy into the combined nucleus to get the free particles; that is why that energy is called the binding energy. The difference in binding energies of the reactants and products of a nuclear reaction can be used to calculate the energy which the reaction will provide.

EXAMPLE 19.11. The mass of a 7 Li nucleus is 7.0154 amu. Using this value and those given above, calculate the energy given off in the reaction of 1 mol of 7 Li:

7 Li + 1 H −→ 2 4 He

Ans. A mole each of the reactant nuclei has a mass of 7.0154 g + 1.00728 g = 8.0227 g. The product has a mass of 2(4.0015 g) = 8.0030 g. The difference in mass, 0.0197 g, has an energy equivalent to

E = mc 2 = (

1.97 × 10 − 5 kg)(3.00 × 10 8 m/s) 2 =

1.77 × 10 12 J More than 1 billion kilojoules of energy is produced from a mole of 7 Li nuclei plus a mole of 1 H nuclei. (Burning a

mole of carbon in oxygen yields 3.93 × 10 5 J.)