Nucleus & Radioactivity, Nuclear Reaction. – SS3 Physics Lesson Note (Second Term)

Radioactivity is the spontaneous decay or disintegration of the nucleus of an atom of an element, during which it emits α, β or γ rays, or any combination of them, together with energy (heat). It is not affected by temperature, pressure or chemical treatment. The half-life is the time taken for half of the atoms present to decay.

Behavioural objectives

By the end of the lesson, students should be able to:

• define radioactivity, half-life and decay constant;
• compare alpha particles, beta particles and gamma rays;
• use the relation between half-life and decay constant, and the decay law, to solve problems;
• write nuclear equations for alpha and beta decay;
• distinguish natural radioactivity from artificial radioactivity and give examples of each.

Lesson contents

• Emission of alpha and beta particles and gamma rays
• Properties and peaceful uses of radioactivity
• Radioactive hazards and safety precautions
• Binding energy

What is radioactivity?

Radioactivity is the spontaneous decay or disintegration of the nucleus of the atom of an element, during which it emits α, β or γ rays, or a combination of any or all three, and energy (or heat).

Separating the radiation from radium

A small sample of radium is placed at the bottom of a small hole drilled in a block of lead. The radiation from the radium comes out of the hole in a narrow beam. A strong magnetic field is placed at the side of the beam, and a photographic plate is placed to receive the rays. The plate shows that the paths of some rays are bent to the right, some to the left and some go straight on, unbent.

Electrically charged plates placed at the side of the beam give the same effect.

• The radiation bent towards the negative electric plate, or the south pole of the magnetic field, is called alpha particles (α-particles).
• The radiation deflected towards the positive electric plate, or the north pole of the magnetic field, is called beta particles (β-particles).
• The radiation that is not affected by the electric or magnetic field is called gamma rays (γ). They are electromagnetic radiation.

How do alpha, beta and gamma radiation compare?

What are radioactive decay, half-life and decay constant?

Radioactivity is a spontaneous process. It goes on independently of external control and is not affected by temperature, pressure or chemical treatment. It is also a random process, because no one can predict which atom will disintegrate at a given time.

The half-life of a radioactive element is the time taken for half of the atoms initially present in the element to decay.

The decay constant

The rate of decay of a radioactive element is proportional to the number of atoms of the material present. If N atoms of a radioactive element are present at a given time, the activity (the number of disintegrations per unit time) is proportional to N:

-dN/dt ∝ N

The minus sign arises because N decreases with time. Introducing a constant of proportionality, λ:

dN/dt = -λN

λ is called the decay constant. Rearranging:

λ = -(1/N)(dN/dt)

Hence, the decay constant is defined as the instantaneous rate of decay per unit atom of a substance:

λ = number of atoms disintegrating per second ÷ number of atoms in the source at that time

The decay law and the half-life relation

By integration:

N = N₀e^-λt

where N₀ is the number of atoms present at t = 0, and N is the number of atoms present at time t.

The half-life, T, is related to the decay constant by:

T = 0.693/λ

Worked example

A certain radioactive element has a half-life of 10 years.

1. How long will it take to lose 7/8 of its atoms originally present?
2. How long will it take until only ¼ of the atoms originally present remain unchanged?

Solution

Half-life = 10 years.

• N/2 remains after 10 years.
• N/4 remains after 20 years.
• N/8 remains after 30 years.

If 7/8 of the atoms have been lost, 1/8 remains. So it takes 30 years to lose 7/8 of the atoms.

N/4 remains unchanged after 20 years.

Answers: (1) 30 years; (2) 20 years.

How are elements transformed by radioactivity?

There are two types of radioactivity:

1. Natural radioactivity
2. Artificial radioactivity

What is natural radioactivity?

Natural radioactivity is the spontaneous disintegration of the nucleus of an atom during which α particles, β particles or γ rays and heat (or energy) are released.

When a radioactive element undergoes radioactive decay, it may emit α, β or γ rays. The emission of an α or β particle changes the atomic number of the element, so a new element is formed.

• ²²⁶₈₈Ra → ⁴₂He + ²²²₈₆Rn + energy (α decay)
• ²²²₈₈Ra → 2 ⁰_-1e + ²²²₉₀Th + energy (two β decays)
• ²³⁸₉₂U → 2 (⁴₂He) + 2 (⁰_-1e) + ²³⁰₉₀Th + energy (two α and two β decays)
• ²³⁴₉₀Th → ⁰_-1e + ²³⁴₉₁Pa + energy (β decay)

In general, α decay is represented by:

^A_ZX → ⁴₂He + ^A-4_Z-2Y + energy

and β decay by:

^A_ZX → ⁰_-1e + ^A_Z+1Y

What is artificial radioactivity?

If radioactivity is induced in an element by irradiation with neutrons, the process is known as artificial radioactivity. Irradiation means exposure to radiation, either by accident or by intent.

In artificial radioactivity, ordinary materials are made radioactive by bombarding them with radioactive particles. Examples:

• ⁴₂He + ¹⁴₇N → ¹⁸₉F → ¹⁷₈O + ¹₁H + energy
• ⁴₂He + ²⁷₁₃Al → ³⁰₁₅P + ¹₀n
• ¹₀n + ⁶₃Li → ³₁H + ⁴₂He + energy
• ¹₀n + ²⁴₁₂Mg → ²⁴₁₁Na + ¹₁H + energy
• ⁴₂He + ⁹₄Be → ¹²₆C + ¹₀n + energy
• ¹₀n + ⁵⁹₂₇Co → ⁶⁰₂₇Co + energy

Isotopes can also be made artificially by bombarding elements with neutrons, protons or deuterons. For example:

• ³⁴₁₆S + ¹₀n → ³⁵₁₆S + energy
• ⁷⁹₃₅Br + ¹₀n → ⁸⁰₃₅Br + energy

Such artificially produced isotopes are unstable and decay with the emission of α-particles, β-particles and γ-rays. They are called radioisotopes.

Evaluation

1. If the half-life of a radioactive substance is 2.45 × 10⁸ s, determine its decay constant.
2. With the aid of a diagram, explain the anomalous behaviour of water.
3. Describe an experiment to determine the apparent cubic expansivity of a liquid.

Assignment

Reading assignment

New School Physics, pages 468 to 471.

Weekend assignment

1. The phenomenon of radioactivity was first discovered by (A) Marie Curie (B) J.J. Thomson (C) Henri Becquerel (D) Niels Bohr (E) Enrico Fermi
2. A radioactive substance has a half-life of 3 days. If a mass of 1.55 g of this substance is left after decaying for 15 days, determine the original value of the mass. (A) 49.6 g (B) 37.2 g (C) 24.8 g (D) 12.4 g
3. Which of the following is usually used to cause fission in an atomic reactor? (A) alpha particles (B) beta particles (C) electrons (D) neutrons
4. A substance has a half-life of 30 minutes. After 6 minutes the count rate was observed to be 400. What was its count rate at zero time? (A) 200 (B) 1200 (C) 1600 (D) 2400
5. A nuclide ²⁰²₈₄Y emits in succession an α-particle and a β-particle. The atomic number of the resulting nuclide is (A) 198 (B) 83 (C) 82 (D) 80

Theory

1. (a) Define radioactivity, half-life and decay constant.
   (b) Write down the relation between half-life and decay constant.
   (c) In 180 minutes, the activity of a certain radioactive substance falls to one-eighth of its original value. Calculate its half-life.
2. (a) A nuclide X emits β-particles to form a daughter nuclide Y. Write a nuclear equation to illustrate charge conservation.
   (b) An isotope of a nuclide has a half-life of 5.4 × 10³ s. Calculate its decay constant.