Question 10.1.Q1: During the past century radioactivity has revolutionized sci......
During the past century radioactivity has revolutionized science, played an important role in industrial development, introduced several new branches of physics, and helped in establishing medical physics as a branch of physics of importance to both physics and medicine.
(a) Define radioactivity and list a few other terms that are used to describe the process.
(b) For the following phenomena name the scientist credited with the discovery and the year of discovery: (1) Natural radioactivity, (2) Radium and polonium, (3) Exponential laws of radioactivity, (4) Artificial radioactivity, and (5) Fission.
(c) Name and define the characteristic parameter that is used to describe a given radioactive process. Discuss the dependence of this parameter on prevailing physical conditions in radioactive atom’s environment.
(d) In a radioactive substance that contains a large number N of identical radioactive atoms, what is the probability that a given atom will decay during a time interval Δt? Are there any restrictions on the magnitude of Δt?
(e) Define activity A of a radioactive substance and state its relationship with the number N of radioactive atoms present in the sample. State the unit of activity in the SI system of units and in the old (traditional) system of units. Also state the relationship between the two systems.
(f) Both hertz (Hz) and becquerel (Bq) are units of a physical quantity and equal to 1/s. What is the difference between the two units and which physical quantities do they represent?
(g) Define specific activity a and show how it is determined for a given radionuclide. State the unit of specific activity in the SI system of units and in the old (traditional) system of units.
(a) Radioactivity is a process by which an unstable parent nucleus transforms spontaneously into one or several daughter nuclei that are more stable than the parent nucleus by having larger binding energies per nucleon than does the parent nucleus. The daughter nucleus may be stable or may also be unstable and decay further through a chain of radioactive decays until a stable nuclear configuration is reached. Radioactive decay is usually accompanied by emission of energetic particles, γ rays or both.
In addition to radioactivity, other terms used to describe spontaneous nuclear decay are radioactive decay, nuclear disintegration, nuclear transformation, and nuclear transmutation.
(b) Discoveries related to radioactivity:
(1) Natural radioactivity: Henri Becquerel (1896).
(2) Radium and polonium: Marie Curie-Skłodowska and Pierre Curie (1898).
(3) Exponential laws of radioactivity: Ernest Rutherford and Frederick Soddy (1902).
(4) Artificial radioactivity: Frédéric Joliot and Irène Joliot-Curie (1934).
(5) Fission: Lise Meitner, Otto Frisch, Otto Hahn, and Friedrich W. Strassmann (1938).
(c) All radioactive decay processes are governed by the same general formalism that is based on the definition of the activity A(t) and on the total radioactive decay constant λ that is a characteristic parameter for each radioactive decay process with dimensions of reciprocal time usually in s^{−1}. The decay constant λ is independent of the age of the radioactive atom and is essentially independent of physical conditions such as temperature, pressure, and chemical state of the atom’s environment.
(d) The total radioactive decay constant λ multiplied by a time interval Δt that is much smaller than 1/λ represents the probability that any particular atom of radioactive substance containing a large number N(t) of identical radioactive atoms will decay in that time interval.
(e) Activity A(t) of a radioactive substance containing a large number N(t) of identical radioactive atoms represents the total number of decays per unit time and is defined as a product between N(t) and decay constant λ, i.e.,
\mathcal{A}(t)=\lambda N(t) (10.1)
SI unit of activity is the becquerel (Bq) defined as 1 \mathrm{Bq}=1 \mathrm{~s}^{-1}. The old unit of activity, the curie (Ci), was initially defined as the activity of 1 g of radium-226 and given as 1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{~s}^{-1}. The activity of 1 g of radium-226 was subsequently measured to be 3.665 \times 10^{10} \mathrm{~s}^{-1}; however, the definition of the curie was kept at 3.7 \times 10^{10} \mathrm{~s}^{-1}. The current value of the activity of 1 g of radium-226 is thus 0.988 Ci or 3.665 \times 10^{10} Bq. The SI unit becquerel and the traditional unit curie are related as follows
1 \mathrm{Ci}=3.7 \times 10^{10} \mathrm{~Bq}=0.037 \mathrm{TBq} \text { and } 1 \mathrm{~Bq}=2.703 \times 10^{-11} \mathrm{Ci} \text {. } (10.2)
(f) Becquerel (Bq) and hertz (Hz) both correspond to 1 s^{−1}; however, becquerel refers to physical quantity “activity” and hertz refers to periodic motion (“frequency”).
(g) Specific activity a of a radioactive substance is defined as the activity A per unit mass m
a=\frac{{A}}{m}=\frac{\lambda N}{m}=\frac{\lambda N_{\mathrm{A}}}{A}=\frac{(\ln 2) N_{\mathrm{A}}}{t_{1 / 2} A}, (10.3)
where N_A is the Avogadro number \left(6.022\times 10^{23}\ mol^{−1}\right), A is the atomic mass number, and t1/2 is the half life of the radioactive substance. The units of specific activity are Bq/kg (SI unit) and Ci/g (traditional unit). The relationship between the two units is given as: 1 Ci/g = 37 TBq/kg.