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The machines in the image are Pressurized Water Reactors (PWRs). These are small nuclear reactors used for the generation of power. Primarily the nuclear energy is used to change water into steam and the steam then runs the machinery. Several hundred PWRs are used for propulsion in military vessels such as aircraft carriers, submarines, and ice breakers. These nuclear reactors were originally designed at the Oak Ridge National Laboratory for use as nuclear submarine power plants.

The total mass of a stable nucleus is always less than the sum of the masses of its constituent protons and neutrons. This is known as mass defect . As an example of this, consider the mass of a $^4_2 He$  nucleus compared to the sum of the masses of its constituent nucleons.

The mass of a $^4_2 He$  nucleus is 4.002603 amu. The mass of two neutrons and two protons is $(2)(1.008665 \ \text{amu}) + (2)(1.007825 \ \text{amu}) = 4.032980 \ \text{amu}$ . Thus, the mass of the helium-4 nucleus is 0.030377 amu less than the masses of its constituents. The lost mass has gone into energy that is called binding energy . The binding energy is equal to the amount of energy that would have to be put into the helium-4 nucleus in order to break it into its constituent protons and neutrons. Without the binding energy, the repulsion between the protons would blow this nucleus apart. We often refer to the average binding energy per nucleon which is defined as the total binding energy of a nucleus divided by the number of nucleons in the nucleus.

Each nucleus, therefore, has competing forces. The repulsive force between the protons tends to blow the nucleus apart and the binding energy tends to hold the nucleus together. If the average binding energy per nucleon overcomes the repulsion, the nucleus stays together and it referred to as stable. If the repulsion overcomes the average binding energy per nucleon, the nucleus may blow apart or undergo nuclear disintegration . When a nucleus disintegrates, it throws off pieces of itself and energy in the form of gamma rays . This disintegration process came to be called radioactivity .

Early researchers in radioactivity found that the emissions from radioactivity could be classified into three distinct types according to their penetrating power. One type of radiation could barely penetrate a sheet of paper. The second type could pass through as much as 3 mm of aluminum. The third type was extremely penetrating and could pass through several centimeters of lead. They named these three types of radiation alpha $(\alpha)$ , beta $(\beta)$ , and gamma $(\gamma)$  respectively. Eventually, each type of radiation was further identified. Alpha particles are the nuclei of helium atoms, $^4_2 He$ . Beta particles are electrons, and gamma rays are very high energy photons (even higher energy than x-rays).

When a nucleus emits an  $\alpha$ particle, the remaining particle will contain two less protons and two less neutrons.  The new particle will have an atomic number two less and a mass number four less than the original nuclide.

$^{226}_{88} Ra \longrightarrow {^{222}_{86}Rn}+ {^4_2 He}$

The daughter product, $^{222}_{86} Rn$ , is different from the parent nucleus, $^{226}_{88} Ra$ , by two protons and two neutrons. This changing of one element into another is called transmutation.

Transmutation also occurs when a nucleus undergoes  $\beta$ decay. An example of beta decay is the emission of an electron by a carbon-14 nucleus.

$^{14}_6 C \longrightarrow {^{14}_7 N}+{^0_{-1} e}$

The symbol ${^0_{-1}e}$  represents an electron whose charge corresponds to  $Z=-1$ and since it has no nucleons, $A=0$ . It must be carefully noted that the electron released during beta decay is NOT an orbital electron but an electron whose origin was in the nucleus. The process has one neutron becoming one proton and one electron and the electron being emitted as a beta particle. Since a neutron has been lost AND a proton has been gained, the mass number does not change. The atomic number, however, has increased one due to the gain of a proton.  Therefore, as a result of beta decay, the daughter product will have the same mass number as the parent and an atomic number one greater than the parent.

#### Summary

• The total mass of a stable nucleus is always less than the sum of the masses of its constituent protons and neutrons. This is known as mass defect.
• The mass lost in mass defect has gone into energy that is called binding energy.
• Each nucleus has competing forces. The repulsive force between the protons tends to blow the nucleus apart and the binding energy tends to hold the nucleus together.
• If the repulsion overcomes the average binding energy per nucleon, the nucleus may blow apart or undergo nuclear disintegration.
• Early researchers in radioactivity found that the emissions from radioactivity could be classified into three distinct types according to their penetrating power. They named these three types of radiation alpha $(\alpha)$ , beta $(\beta)$ , and gamma  $(\gamma)$ respectively.
• When a nucleus emits an  $\alpha$ particle, the remaining particle will contain two less protons and two less neutrons.
• As a result of beta decay, the daughter product will have the same mass number as the parent and an atomic number one greater than the parent.

#### Practice

Questions

1. Why does the Geiger counter record clicks even when there is no radioactive source present?
2. What is the charge on an alpha particle?
3. What is the charge on a beta particle?

#### Review

Questions

1. Write the nuclear equation showing beta decay of a copper-64 nucleus.
2. Write the nuclear equation showing the alpha decay of a uranium-238 nucleus.
3. What element is formed by the beta decay of sodium-24?
4. What element is formed by the alpha decay of bismuth-211?