B.Sc. (H.
) Physics (Section –II)
Semester IV
Elements of Modern Physics (2019-20)
Radioactivity
by
Sonia Lumb
Radioactivity: Discovery
1896: Antoine Henri Becquerel 1899: Ernest Rutherford,
French Engineer, Physicist, British physicist identified
Nobel laureate was the first two kinds of rays
person to discover evidence of emanating from radioactive
radioactivity. substances and named
them alpha and beta rays.
Photos: https://en.wikipedia.org/
Radioactivity: The phenomenon of spontaneous decay of a nucleus accompanied by
the emission of alpha particles, beta particles or gamma-rays is known as radioactivity.
It can be either natural or artificial.
Most elements in nature have no radioactive isotopes.
Some elements have some stable isotopes and some radioactive ones, e.g., potassium.
Some elements have only radioactive isotopes, e.g., uranium.
Features extraordinary from the perspectives of classical physics:
• When a nucleus undergoes alpha or beta decay, its atomic number Z changes and it
becomes the nucleus of a different element. Thus the elements are not immutable.
• The energy liberated during radioactive decay comes from within individual nuclei
without external excitation. Einstein’s proposed equivalence of mass and energy
could solve this puzzle.
• Radioactive decay is a statistical process that obeys the laws of chance. No cause-
effect relationship is involved in the decay of a particular nucleus.
The experiments of Rutherford and his co-workers, distinguished three components in
the penetrating radiations emitted from radionuclides. These components were called
alpha, beta and gamma rays.
In the presence of a magnetic field:
• Alpha particles (4He2 nuclei) are deflected to the left, hence they are positively
charged;
• Beta particles (electrons) are deflected to the right, hence they are negatively charged;
• Gamma rays (high-energy photons) are not affected, hence they are unchanged.
• Alpha particles from radioactive materials are stopped by a piece of cardboard.
• Beta particles penetrate the cardboard but are stopped by a sheet of aluminum.
• Even a thick slab of lead may not stop all the gamma rays.
Various decay modes of radioactive nuclei.
Activity: The rate at which the nuclei of the radioactive sample decay.
If N is the number of nuclei at a certain time t,
Activity (R) = - dN/dt
The minus sign is used to make R a positive quantity.
Units of activity:
• becquerel (SI unit of activity is named after Becquerel.)
1 becquerel = 1 Bq = 1 decay/s
Megabecquerel (1 MBq =10^6 Bq), Gigabecquerel (1 GBq = 10^9 Bq)
• curie (Ci) (Traditional unit of activity.)
1 curie = 1 Ci = 3.70 * 10^10 decays/s = 37 GBq
Radiation dosage is measured in sieverts (Sv).
1 Sv is the amount of any radiation that has the same biological effect as those produced
when 1 kg of body tissue absorbs 1 joule of x-rays or gamma rays.
The chief sources of radiation dosage averaged around the world.
Laws of radioactive disintegration:
• There is an equal probability for all nuclei of a radioactive element to decay.
• The rate of spontaneous disintegration of a radioactive element is proportional to the
number of nuclei present at that time.
𝑑𝑁
∝𝑁 (3.1)
𝑑𝑡
N: number of atoms present at time t.
Removing proportionality sign, we get
𝑑𝑁
= −λ𝑁 (3.2)
𝑑𝑡
λ: decay constant of the element.
Negative sign indicates that as t increases N decreases.
Rewriting Eq. (3.2) as
𝑑𝑁
= −λ𝑑𝑡 (3.2)
𝑑𝑡
𝑑𝑁
Integrating both sides, we have =−λ 𝑑𝑡
𝑁
The exponential nature of this equation shows that it takes an infinite time for the
whole of the radioactive material to disintegrate.
R = - dN/dt = λN
Substituting for N from Eq. (3.6)
N = N0 e-λt
R = λ N0 e-λt
Substituting R0 = λ N0
R = R0 e-λt Activity Law
R0 is the activity at t = 0.
The exponential factor shows that the activity is decreasing in the same fashion as N.
HALF-LIFE
Every radionuclide has a characteristic half-life.
After a half-life has elapsed, that is, when t = T1/2, the activity R drops to ½ R0 by definition.
Average (Mean) Life
The average life is calculated by summing the lives of all the nuclei and dividing by
the total number of nuclei. Suppose dN1 nuclei decay in time t1, dN2 nuclei decay in
time t2, dN3 nuclei decay in time t3 and so on, then the average life or mean life will
be 𝒕𝟏𝒅𝑵𝟏 + 𝒕𝟐𝒅𝑵𝟐 + 𝒕𝟑𝒅𝑵𝟑 + ⋯
τ=
𝒅𝑵𝟏 + 𝒅𝑵𝟐 + 𝒅𝑵𝟑 + ⋯
In integral form
𝑵𝟎 𝑵𝟎
𝟎
𝒕 𝒅𝑵 𝟏
τ= 𝑵𝟎
= 𝒕 𝒅𝑵
𝒅𝑵 𝑵𝟎 𝟎
𝟎
Q. How long does it take for 60.0 percent of a sample of radon to decay? (T1/2 = 3.8d.)
Q. Find the activity of 1.00 mg of radon, 222Rn, whose atomic mass is 222 u and T1/2 = 3.8d.
Reference Books:
• Concepts of Modern Physics, Arthur Beiser, 2002, McGraw-Hill.
• Introduction to Nuclear and Particle Physics, V. K. Mittal, R. C.
Verma, S. C. Gupta, 3rd Edition, PHI Learning Private Limited.
Thanks
