Classwork Series and Exercises {Physics – SS3}: Radioactive Decay

Physics SS 3 Week 2

Topic: Radioactive Decay

Introduction

Radioactive decay is the spontaneous radioactive disintegration of an atomic nucleus, resulting in the release of energy. Some atoms are stable. Others are unstable and ‘decay’, emitting radiation to achieve a stable state. The emissions from an unstable atom’s nucleus, as it decays, can be in the form of alpha, beta or gamma radiation.

 When an atom decays, it changes into another isotope, or form, of the same element or into a completely different element, in a process called transmutation. Different isotopes of the same element differ in the number of neutrons in their nuclei. Some elements reach stability via a series of steps through several isotopes, or ‘daughter products’.

 One example is uranium-238 (U-238), which, through the process of radioactive decay, will eventually become a stable isotope of lead. However, this process takes billions of years. Along the way, as the U-238 isotope’s initial energy declines, it will transmute via a series of elements, each more stable than the last – thorium, radium, radon, polonium and bismuth – before it stabilizes as lead.

 Alpha decay

In alpha decay, a positively-charged particle is emitted from the nucleus of an atom. This alpha particle consists of two protons and two neutrons (the same structure as a helium-4 nucleus). Although alpha particles are normally highly energetic, they travel only a few centimeters in air and are stopped by a sheet of paper or the outer layer of dead skin.

Beta decay
In beta decay, a particle is emitted from the nucleus of an atom. This beta particle is an electron with either negative or positive electric charge. Beta particles may travel metres in air and several millimetres into the human body. Most beta particles may be stopped by a small thickness of a light material such as aluminium or plastic.

Gamma decay

Gamma decay occurs because the nucleus of an atom is at too high an energy state. The nucleus ‘falls down’ to a lower energy state, emitting a high energy photon known as a gamma particle in the process. Gamma particles travel in a wave-like pattern at the speed of light. They can only be stopped by a dense material such as lead, steel, concrete or several metres of water.

Half Life of Radioactive Elements

The half-life of a radioactive element is the time that it takes for one half of the atoms of that substance to disintegrate into another nuclear form. The decay of an isotope can be measured by its half life. These can range from mere fractions of a second, to many billions of years.

Element	Most Stable Isotope	Half-life of Most Stable Isotope
Polonium	Po-209	102 years
Astatine	At-210	8.1 hours
Radon	Rn-222	3.82 days
Radium	Ra-226	1600 years
Thorium	Th-229	7.54 x 104 years
Uranium	U-236	2.34 x 107 years
Protactinium	Pa- 234	1.18 minutes

Example Rate of Radioactive Decay Problem

²²⁶₈₈Ra, a common isotope of radium, has a half-life of 1620 years. Knowing this, calculate the first order rate constant for the decay of radium-226 and the fraction of a sample of this isotope remaining after 100 years.

Solution

The rate of radioactive decay is expressed by the relationship: k = 0.693/t_1/2

Where k is the rate and t_1/2 is the half-life.

Plugging in the half-life given in the problem: k = 0.693/1620 years = 4.28 x 10^-4/year

Radioactive decay is a first order rate reaction, so the expression for the rate is:

log₁₀ X₀/X = kt/2.30

Where X₀ is the quantity of radioactive substance at zero time (when the counting process starts) and X is the quantity remaining after time t. k is the first order rate constant, a characteristic of the isotope that is decaying. Plugging in the values:

log₁₀ X₀/X = (4.28 x 10^-4/year)/2.30 x 100 years = 0.0186

Taking antilogs: X₀/X = 1/1.044 = 0.958 = 95.8% of the isotope remains

Nuclear Reactions

Rutherford in 1919 transmitted nitrogen isotope into an oxygen isotope. The nitrogen was subjected to the action of swift alpha – particles derived from radium salt.

Transmutation is the process by which radioactive elements change into different elements.

Nuclear reaction is a process in which two nuclei or nuclear particles collide, to produce different products than the initial particles.

Nuclear fission and nuclear fusion both are nuclear phenomena that release large amounts of energy, but they are different processes which yield different products. Learn what nuclear fission and nuclear fusion are and how you can tell them apart.

Nuclear Fission

Nuclear fission takes place when an atom’s nucleus splits into two or more smaller nuclei. These smaller nuclei are called fission products. Particles (e.g., neutrons, photons, alpha particles) usually are released, too. This is an exothermic process releasing kinetic energy of the fission products and energy in the form of gamma radiation. Fission may be considered a form of element transmutation since changing the number of protons of an element essentially changes the element from one into another.

Nuclear Fission Example:

²³⁵₉₂U + ¹₀n → ⁹⁰₃₈Sr + ¹⁴³₅₄Xe + 3¹₀n

Nuclear Fusion

Nuclear fusion is a process in which atomic nuclei are fused together to form heavier nuclei. Extremely high temperatures (on the order of 1.5 x 10⁷°C) can force nuclei together. Large amounts of energy are released when fusion occurs.

Nuclear Fusion Examples

The reactions which take place in the sun provide an example of nuclear fusion:

¹₁H + ²₁H → ³₂He

³₂He + ³₂He → ⁴₂He + 2¹₁H

¹₁H + ¹₁H → ²₁H + ⁰₊₁β

Comparison between Nuclear Fission and Fusion

	Nuclear Fission	Nuclear Fusion
Definition:	Fission is the splitting of a large atom into two or more smaller ones.	Fusion is the fusing of two or more lighter atoms into a larger one.
Natural occurrence of the process:	Fission reaction does not normally occur in nature.	Fusion occurs in stars, such as the sun.
Byproducts of the reaction:	Fission produces many highly radioactive particles.	Few radioactive particles are produced by fusion reaction, but if a fission “trigger” is used, radioactive particles will result from that.
Conditions:	of the substance and high-speed neutrons are required.	High density, high temperature environment is required.
Energy Requirement:	Takes little energy to split two atoms in a fission reaction.	Extremely high energy is required to bring two or more protons close enough that nuclear forces overcome their electrostatic repulsion.
Energy Released:	The energy released by fission is a million times greater than that released in chemical reactions; but lower than the energy released by nuclear fusion.	The energy released by fusion is three to four times greater than the energy released by fission.
Nuclear weapon:	One class of nuclear weapon is a fission bomb, also known as an atomic bomb or atom bomb.	One class of nuclear weapon is the hydrogen bomb, which uses a fission reaction to “trigger” a fusion reaction.

Uses of Radioactivity

1. Radioactivity tracers are commonly used in the medical field and also in the study of plants and animals.
2. Radiation is used and produced in nuclear reactors, which controls fission reactions to produce energy and new substances from the fission products.
3. Radiation is also used to sterilize medical instruments and food.
4. Radiation is used by test personnel who monitor materials and processes by non-destructive methods such as x-rays.

Comparison of Nuclear Reaction and Ordinary Chemical Reaction

Nuclear Reaction	Ordinary Chemical Reaction
During nuclear reactions, the nuclei of atoms undergo change and therefore new elements are formed as a result of such reactions.	During chemical reactions, elements do not lose their identity. In these reactions, only the electrons in the outermost shell of atoms participate whereas the nuclei of atoms remain unchanged.
Reactivity of an element towards nuclear reactions is nearly independent of oxidation state of the element. For example, Ra element or Ra2+ ion in RaC2 behave s similarly during nuclear reactions.	Reactivity of an element towards chemical reactions depends upon the oxidation state of the element. In ordinary chemical reactions, Ra and Ra2+ behave quite differently.
In nuclear reactions, isotopes behave quite differently. For example, U-235 undergoes fission quietly readily but U-238 does not.	Different isotopes of an element have nearly same chemical reactivity.
Rate of a nuclear reaction is independent of temperature and pressure.	Rate of a chemical reaction is largely affected by temperature and pressure.
A nuclear reaction cannot be reversed.	A chemical reaction can be reversed.
Nuclear reactions are accompanied by large energy changes.	Chemical reactions are accompanied by relatively small energy changes.