Lesson plan

Topicm0e1778b7e7a45fdf_1528449000663_0Topic

Nuclear transformations

Levelm0e1778b7e7a45fdf_1528449084556_0Level

Third

Core curriculumm0e1778b7e7a45fdf_1528449076687_0Core curriculum

XI. Nuclear physics. The student:

5) describes the decay of a radioisotope; uses the concept of half‑life.

Timingm0e1778b7e7a45fdf_1528449068082_0Timing

45 minutes

General learning objectivesm0e1778b7e7a45fdf_1528449523725_0General learning objectives

Describes the decay of radioactive isotope.

Key competencesm0e1778b7e7a45fdf_1528449552113_0Key competences

1. Explains the concept of half‑life.

2. Explains the law of radioactive displacements.

Operational (detailed) goalsm0e1778b7e7a45fdf_1528450430307_0Operational (detailed) goals

The student:

- describes the statistical behaviour of the radioactive decay,

- uses the concept of half‑life.

Methodsm0e1778b7e7a45fdf_1528449534267_0Methods

1. Discussion.

2. Reading the information from a graph.

Forms of workm0e1778b7e7a45fdf_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm0e1778b7e7a45fdf_1528450127855_0Introduction

The students remind what radioactive decay is and what the properties of alpha, beta and gamma radiation are.

What is radioactive decay? What properties has alpha, beta and gamma radiation?

Procedurem0e1778b7e7a45fdf_1528446435040_0Procedure

The teacher introduces the concept of statistical description of radioactive decay.

Radioactive decayradioactive decayRadioactive decay is an random process in which alpha, beta or gamma radiation is emitted. It is not possible to predict when an individual atom will decay. The decay process is spontaneous and can be only described statistically.

Law of Radioactive Decay:

The law of radioactive decay describes the statistical behaviour of a large number of nuclides. It says that:

∆ N = - λ \cdot N (t) \cdot ∆ t

where:
N(t) - is the total amount of untransformed nuclei at a time t,
∆N - is the number of nuclei decayed in the time ∆t.

The decay constantdecay constantdecay constant $λ$ is a parameter that characterizes a given radioactive substance. It determines the probability of nucleus decay per unit of time. The unit of the decay constant is sIndeks górny -1.

The radioactivity of an object is measured by the number of nuclear decays it emits each second – the more it emits, the more radioactive it is.

The decay rate is known as the activity of a particular sample and is defined as a number of decays in nucleus at any given moment:

A (t) = \frac{∆ N}{∆ t}

The basic unit of activity is the becquerel (Bq):

1 B q = \frac{1 d e c a y}{1 s}

Half‑life:
The rate of radioactive decayradioactive decayradioactive decay is also determined in terms of half‑lives. The half‑life is the amount of time it takes for a given isotope to lose half of its radioactivity and is denoted as T or TIndeks dolny 1/2. After two half‑lives the size of the sample is quartered, after third half‑life an eighth of atoms is left intact and so on. The half‑life does not depend on the age of the nuclei or the amount of the sample.

The dependence of the number of nuclei remaining in a given isotope sample on time has an exponential character.

[Illustration 1]

Using the half‑life concept, the law of radioactive decayradioactive decayradioactive decay can be written down as:

N (t) = N_{0} \cdot 2^{- \frac{t}{T_{\frac{1}{2}}}}

This dependence allows calculating the number of non‑transformed nuclei at any time.

In the table below half‑lives for different isotopes are presented.

[Table 1]

The students analyze the decay curve.

Task 1

Examine the graph showing the radioactive decay for the isotope ${}^{14}C$ in the sample of organic material for 30000 years after its death. Answer the questions.

1. How long is approximately one half‑life for ${}^{14}C$ ?

2. If the initial number of the atoms of ${}^{14}C$ in the sample was 10000, how many atoms that are not transformed remains after:

a) One half‑life.
b) Two half‑lives.
c) Three half‑lives.

3. Explain why in your opinion ${}^{14}C$ half‑life measurements are not effective in dating of a sample of a living organism in the time period longer than 50000 years after its death?

[Illustration 2]

Law of radioactive displacements:
In the process of a radioactive disintegrationdisintegrationdisintegration, the nucleus which undergoes decay is called a parent nucleusparent nucleusparent nucleus and the product of the process is called a daughter nucleusdaughter nucleusdaughter nucleus.

The law of radioactive displacements, also known as Fajans and Soddy Law describes the relations between the parent nucleusparent nucleusparent nucleus and daughter nucleusdaughter nucleusdaughter nucleus in terms of the atomic number and the mass number.

$α$ -decay:

In alpha decay, an element is created with an atomic number less by 2 and a mass number less by four of that of the parent radioisotope. The $α$ -decay can be expressed as:

{}_{Z}^{A}X \to {}_{Z - 2}^{A - 4}Y + {}_{2}^{4}H e

Example:

Radium ${}_{88}^{226}R a$ is converted to radon ${}_{86}^{222}R n$ due to $α$ -decay.

{}_{88}^{226}R a \to {}_{86}^{222}R n + {}_{2}^{4}H e

$β$ −decay:

In beta decay (emitted particle is an electron), the mass number remains unchanged while the atomic number becomes greater by 1 than that of the parent radioisotope. $β$ −decay can be expressed as:

{}_{Z}^{A}X \to {}_{Z + 1}^{A}Y + {}_{-1}^{0}e

Example:

Thorium ${}_{90}^{234}T h$ is converted to protoactinium ${}_{91}^{234}P a$ due to $β$ -decay.

{}_{90}^{234}T h \to {}_{91}^{234}P a + {}_{-1}^{0}e

At a time, either $α$ or $β$ particle is emitted. Both $α$ and $β$ particles cannot be emitted simultaneously during a single decay.

$γ$ −decay:

When a radioactive nucleus emits $γ$ −rays, only the energy level of the nucleus changes and the atomic number and mass number remain the same.

During $α$ or $β$ −decay, the daughter nucleusdaughter nucleusdaughter nucleus is mostly in the excited state. Return to the ground state is associated with the emission of $γ$ −rays.

Example:

During the transformationtransformationtransformation of radium ${}_{88}^{226}R a$ into radon ${}_{86}^{222}R n$ , radon returns from the excited state to the ground state and $γ$ −ray of 0.187 MeV is emitted.

[Interactive graphics]

Radioactive series:
A radioactive seriesradioactive seriesradioactive series is a decay chain in which each member of the series is a product of the decay of the nuclide before it. The series ends with a stable nuclide. Four radioactive seriesradioactive seriesradioactive series are known: three of them occur naturally, the other one starts with an artificially created radionuclide.

Natural series:

- Thorium ${}^{232}T h$ ,

- Uranium ${}^{235}U$ ,

- Uranium ${}^{238}U$ .

All of them end with an isotope of lead.

The plutonium series starts with the artificial plutonium isotope ${}^{241}P u$ and ends with bismuth ${}^{209}B i$ .

[Illustration 3]

Task 2

Write the equations for the following processes:
1. The alpha decay of radon ${}^{198}R n$ .
2. The beta decay of uranium ${}^{237}U$ .m0e1778b7e7a45fdf_1527752263647_0Write the equations for the following processes:
1. The alpha decay of radon ${}^{198}R n$ .
2. The beta decay of uranium ${}^{237}U$ .

Lesson summarym0e1778b7e7a45fdf_1528450119332_0Lesson summary

Radioactive decay is a spontaneous process where alpha, beta or gamma radiation is emitted. The description of such a process is done in a statistical approach. The law of radioactive decay, half‑life and the law of radioactive displacement describe features of disintegration of a given isotope.
The law of radioactive decay describes the statistical behaviour of a large number of nuclides.m0e1778b7e7a45fdf_1527752256679_0Radioactive decay is a spontaneous process where alpha, beta or gamma radiation is emitted. The description of such a process is done in a statistical approach. The law of radioactive decay, half‑life and the law of radioactive displacement describe features of disintegration of a given isotope.
The law of radioactive decay describes the statistical behaviour of a large number of nuclides.

Selected words and expressions used in the lesson plan

transformationtransformationtransformation

radioactive decayradioactive decayradioactive decay

decay constantdecay constantdecay constant

half‑livehalf‑livehalf‑live

radioactive seriesradioactive seriesradioactive series

nuclidenuclidenuclide

disintegrationdisintegrationdisintegration

displacementdisplacementdisplacement

parent nucleusparent nucleusparent nucleus

daughter nucleusdaughter nucleusdaughter nucleus

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radioactive decay1

decay constant1

transformation1

disintegration1

parent nucleus1

daughter nucleus1

radioactive series1

half‑live1

nuclide1

displacement1

Scenariusz

Topicm0e1778b7e7a45fdf_1528449000663_0Topic

Lesson stages

Selected words and expressions used in the lesson plan