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RADIOACTIVITY PHYSICS SIMPLIFIED NOTES

November 19, 2024

RADIOACTIVITY

Table of Contents

INTRODUCTION

In 1896 Henri Becquerel accidently discovered that Uranium salt crystals emitted invisible radiation that darkened a photographic plate even when covered to exclude light.
Madame Curie & her husband Pierre discovered Polonium & Radium.
Marie Curie described these elements as being radioactive and concluded that the radiations originate from the nucleus. They called this phenomenon

Radioactivity or radioactive decay is the spontaneous disintegration of unstable nuclides to form stable ones with the emission of radiation. Unstable nuclides continue to disintegrate until a stable atom is formed.

ATOMIC STRUCTURE

The nucleus of an atom has a specific number of protons and neutrons. The number of protons in the nucleus is called the atomic or proton number while the sum of the number of protons and neutrons is called the mass or nucleon number.

An atom X of mass number A and atomic number Z can be represented as . If the number of neutrons in the nucleus is N, then:

A= Z+N.

Thus, hydrogen can be represented by , helium by and neon by . Some atoms have the same number of protons in the nucleus yet different mass numbers. Such atoms are referred to as isotopes. Examples of isotopes include carbon- 12 and carbon- 14. Isobars – are nuclides with the same mass number A but different atomic number Z – Ra, Ac. Th.

The energy holding the protons and neutrons together in the nucleus is called the binding or nuclear energy.

The masses of atoms are conveniently given in terms of atomic mass units (u) where (u) is 1/12th the mass of one atom of carbon-12 and has a value of 1.660 × 10-27 kg. Hence the mass of one proton is equal to 1.67 × 10-27 and is equal to 1u.

NUCLEAR STABILITY

When the ratio of the number of protons to the number of neutrons in a nucleus is about 1:1, the nuclide is said to be stable, otherwise it is an unstable. For unstable nucleus, it has to undergo disintegration in an attempt to achieve stability. Below is a stability curve;

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From the graph, it is observed that the unstable nuclides are outside the stability line. Those nuclides above the stability line have too many neutrons; hence decay in such a way that the proton number increases. Those below the stability line have too many protons and therefore decay in such a way that their proton number decreases.

TYPES OF RADIACTIONS

In the process of disintergration of radioactive elements, there are three radiations which may be emitted namely;

Alpha (α) radiations
Beta (β) radiations
Gamma (γ) radiations.

Radiations emitted by radioactive elements are identified according to the properties they exhibit. Their behavior can be observed when they are passed through a magnetic or an electric fields

Similarly, their behavior can be observed when they are passed through a field as shown below:

ALPHA (α) RADIATIONS:

Are positively charged.
Are massive or heavy and thus have shorter range in air. They are slightly deflected by strong magnetic or electric field due to their higher mass.
Cause the highest ionization effect on the particles on their paths compared to beta and gamma radiations, thereby losing most of their energy.
Have the least penetrating ability or power compared to the other two radiations. They can be stooped by a thick sheet of paper.

BETA RADIATIONS:

Are negatively charged.
Are lighter compared to alpha radiations. Hence they are greatly deflected by strong magnetic or electric field.
Have longer range in air.
Cause less ionization compared to alpha radiations. Hence they have a higher penetrating ability or power. They can penetrate a thick sheet of paper but can be stopped by a thin aluminium foil.

GAMMA RADIATIONS:

Are massless and do not have charge. Hence they are not deflected by both magnetic and electric fields.
Are electromagnetic waves.
Cause very little ionization. Hence most of their energy is intact. They have the highest penetrating ability or power of all the three radiations. They can penetrate thick paper and aluminium but is stopped by thick lead.

COMPARISONS OF THE THREE RADIATIONS

Range in air
α-particles – are the least penetrating of the three radiations.

They have a few cm in air about 5 cm.

β-particles – are more penetrating than alpha particles.

Several metres in air – 5m

g-rays – are the most penetrating of the three. Hardly affected by air. Intensity reduces as they spread.
Absorption
α-particles – are stopped by very thin aluminium, paper or skin.
β-particles – can pass through 1 mm of aluminium: -stopped by a few mm of aluminium or Perspex.
g-rays – can pass through metal and even several mm of lead but stopped by 5 cm of lead.

N/B 1 cm thickness of lead is referred to as the half-thickness for the lead since it lowers the intensity of the radiation to half the original volume. Gamma rays are similar to the x-rays, but they have a generally shorter wavelength. The main difference between X-rays and gamma rays is that gamma rays originate from energy changes in the nucleus of atoms while X-rays originate from energy changes associated with electron structure of atoms.

Effect of electric field
α-particles – Small deflection.

Attracted towards the negative plate, indication a (+ve) charge.

β-particles – Strongly deflected.

Attracted towards the positive plate indicating a (-ve) charge – use Fleming’s left hand rule for direction of force.

g-rays – Not affected by an electric field. Indicating no charge.
Effect of magnetic field
α-particles – Deflected by magnetic field, but only a powerful field has an effect, indicating that the particles are relatively heavy.
-The positive charge which they carry results in their deflection in the opposite direction to beta-particles.
β-particles – They are strongly deflected by magnetic field because of their lower mass or light mass
g-rays – They are not affected by magnetic field and carry on straight as the speed of light.
Ionization effects

When alpha, beta or gamma radiations pass through air, they knock off electrons from air molecules resulting in the formation of positive ions. This effect is called ionisation.

Therefore, if electrons become detached from molecules in a gas, ions are produced and the gas is ionized.

α-particles – They are very strong ionizers as they are able to knock off more electrons as they pass through air. They discharge electroscope rapidly.
β-particles – Cause less ionization, about 1/10^th that of α-particles. Discharge electroscope slowly.
g-rays – Cause negligible ionization1/1000^th of alpha. Does not discharge electroscope.

Table below shows the characteristics of alpha particle, beta particle, and gamma particle.

Characteristic	Alpha particle	Beta particle	Gamma particle
Nature	Positively charged helium nucleus, He	Negatively charged electron, e	Neutral
In an electric field	Bends to the negative plate	Bends to the positive plate	Does not bend, showing that it is neutral.
In magnetic field	Bends a little showing that it has a big mass. Direction of the bend indicates that it is positively charged.	Bends a lot showing that it has a small mass. Direction of the bend indicates that it is negatively charged.	Does not bend showing that it is neutral.
Ionising power	Strongest	Intermediate	Weakest
Penetrating power	low	Intermediate	High
Stopped by	A thin sheet of paper	A few millimeters of aluminium	A few centimeters of lead or concrete
Range in air	A few centimeters	A few metres	A few hundred metres
Speed	1/20 X the speed of light, c	3%-99% of the speed of light, c	The speed of light, c

RADIOACTIVITY

Radioactivity is the spontaneous emission of the particles from the nucleus of an unstable nuclide.

It can also be defined as the spontaneous disintegration of unstable nuclides to form stable ones with the emission of radiation

Radioactive decay is the disintegration of certain naturally occurring nuclides with emission of α, β and g-rays.

Radioactive decay involves the emission of Alpha and Beta particles but sometimes extra energy is released as Gamma rays.

Note that a particular radioactive decay process must not necessarily emit all the three radiations.

Radioactive decay is not dependent on physical factors like pressure, temperature or chemical composition of the nuclide.

There are three types of radioactive decay:

ALPHA DECAY

This decay process emits alpha radiation(s). Alpha radiation is the nucleus of a helium atom represented by . If a nuclide decays by releasing an alpha particle, the mass number of the parent nuclide is reduced by 4 while atomic number is reduced by 2. This is expressed as;

(Parent nuclide) (Daughter nuclide) (Alpha nuclide)

For example, Uranium 238 decays to Thorium 234 by emitting an alpha particle. The decay is expressed as;

Similarly, polonium undergoes alpha decay to become lead.

BETA DECAY

When an atom undergoes beta decay, it emits a beta particle. A beta particle is a fast moving electron represented by . The mass number of such a nuclide remains the same while its atomic number increases by one (1). This is expressed as:

(Parent nuclide) (Daughter nuclide) (Beta nuclide)

Radioactive sodium, for example undergoes beta decay to become magnesium. This is written as;

GAMMA DECAY

Gamma decay does not have any effect on the mass number or atomic number of the nuclide. Instead the nuclide attains stability by simply releasing energy in the form of gamma radiation.

For example,;

Cobalt-60;

Thorium-230;

Example 1

Thorium-230 [ ] undergoes decay to become Randon-222[ ]. Find the number of alpha particles emitted.

SOLN

Let the number of alpha particles emitted be x. the expression for the decay is;

Thus;

4x +222 = 230 OR 2x + 86 = 90

4x = 8 2x = 4

Hence, x = 2 x = 2

Two alpha particles are emitted.

Example 2

Lead-214 ( ) decays to polonium-214( ) by emitting β-particles. Calculate the number of β-particles emitted.

SOLN

Let x be the number of β-particles emitted.

+ X ( )

82 = 84-x

X = 2

Two β-particles are emitted.

Example 3

Uranium-238 ( ) undergoes a decay emitting alpha and beta particles to become lead-206 ( ). Calculate the number of alpha and beta particles emitted.

SOLN

Let the number of α and β-particles emitted be x and y respectively

238 = 206+4x

4x = 32

X = 8

Also;

92 = 82+2x-y

92 = 82 + 16 – y

92 = 98 – y

Y = 6

Eight alpha particles and 6 beta particles are emitted.

Example 4

Uranium ( ) decays to polonium ( ) by emitting alpha particles. Write down the nuclide equation to represent the decay process. Hence determine the number of alpha particles emitted.

SOLN

+ X ( )

234 = 218+4x

4X =16

X = 4

Alternatively,

92 = 84+2x

X =8/2 =4

The decay equation is therefore;

+ 4 ( )

RADIATION DETECTORS

Below are some of the radiation detectors:

A PHOTOGRAPHIC EMULSIONS

All the three radiations affect photographic emulsion or plate. When radioactive radiations strike a photographic film, they cause photographic emulsion i.e the film is blackened.

Photographic films are very useful to workers who handle radioactive materials. The workers are given special badges which contain small piece of unexposed photographic film. This will darken when exposed to radioactive radiations and hence a safety precaution should be taken.

THE LEAF ELECTROSCOPE

We have already seen that alpha and beta particles can ionize particles on their paths. This produces ions. If a source of these radiations is brought near the cap of a charged electroscope, the electroscope repels ions of similar charge but attracts those of the opposite charge. This neutralizes the electroscope and the leaf falls.

This method is most suitable for alpha particles since they cause the highest ionization but is not suitable for gamma radiations because they cause the least ionization.

CLOUD CHAMBER

When air is cooled until the vapour it contains reaches saturation, it is possible to cool it further without condensation occurring. Under these conditions, the vapour is said to be super-saturated. This can only occur if the air is free of any dust, which normally acts as nuclei for condensation. The ionization of air molecules by radiation can be investigated by a cloud chamber. The common types of cloud chambers include;

Expansion cloud chamber
Diffusion cloud chamber

EXPANSION CLOUD CHAMBER

When a radioactive element emits radiations into the chamber, the air inside is ionized.

If the piston is now moved down suddenly, air in the chamber will expand and cooling occurs. When this happens, the ions formed act as nuclei on which the saturated alcohol or water vapour condenses, forming tracks.

THE DIFFUSION CLOUD CHAMBER

The common diffusion chamber is made up of a cylindrical transparent container. It is partitioned into two compartments by a blackened metal plate. The upper compartment is fitted with the transparent Perspex lid and its top lined with a thin strip of felt ring soaked in alcohol or water. The bottom is fitted with sponge and closed with removable cover. The upper compartment contains air, which is at the room temperature at the top. The air at the bottom is at about -78⁰C due to a layer of dry ice in the lower compartment. The felt ring is soaked in alcohol. This alcohol vapourizes in the warm region, diffuse down and is then cooled.

Black metal base Perspex lid Radioactive source

Felt ring soaked in alcohol

Light source

Dry ice [solid carbon (iv) oxide]

Sponge

Wedge

Removable base

This detector uses the concept that when an ionizing radiation passes through air with saturated vapour, then the vapour is observed to condense on the ions formed. This explains why aeroplanes sometime leave trails of cloud behind them as they move through super saturated air.

In the diffusion cloud chamber, alcohol vaporizes and diffuses towards black metal base. When a charged particle from the radioactive source; either alpha or beta particle, knocks the air particles ions are produced. The vaporized alcohol condenses on the formed ions. Since positive ions are heavy, they remain behind forming tracks which can be clearly seen through the Perspex lid. To enhance visibility, a source of light is used to illuminate the chamber.

The dry ice is used to keep the black metal base cool while the sponge is used to keep the dry ice in contact with the black metal base.

Each radiation will produce a specific track as shown below:

Tracks due to alpha radiation

They are short, straight and thick due to the following:

Alpha particles cause heavy ionization, rapidly losing energy, hence shorter range in air.
They are massive and their path cannot therefore be changed by air molecules. It is not easy to displace them from their path by air particles.
They cause more ions on their paths as they knock off more elecrons

Tracks due to beta radiation

They are generally thin and irregular in direction due to:

Their longer range in air.
They are lighter due to their lower mass.
Irregular in direction (not straight), meaning that they can be displaced by air particles. They are also repelled by electrons of atoms within their path.

Tracks due to gamma radiation

Tracks due to gamma radiation are generally scanty and disjointed. These tracks do not come directly from the source but from electrons released by the gas atoms when they are struck by gamma radiation. The electrons then produce their own tracks.

THE GEIGER MULLER (GM) TUBE

The tube consists of a thin mica (or aluminium) window at one end of a closed glass tube which contains argon gas and little bromine gas at low pressure. A thin wire runs through the centre of the tube and is connected to the positive terminal of a high voltage supply. The walls of the tube are coated with a conductor and connected to negative terminal of the power supply.

When a radioactive substance is placed in front of the window, the radiation enters the tube through the thin mica window. The radiation ionizes argon gas. Opposite ions are attracted to either the cathode or the anode making a pulse of current to flow. As these ions move towards either electrode, they continue ionizing the argon gas producing more ions. The current is passed through an amplifier and then to a ratemeter where it is registered.

Note that only one pulse should be registered for each ionizing particle entering the tube. However, due to the high energy content of the positive ions, more electrons may be liberated from the surface of the cathode when struck by the positive ions. Such electrons are called secondary electrons. The secondary ionization causes the formation of avalanche of electrons. These can cause further ionization rendering the pulse registered incorrect.

To counter this, bromine is used which acts as a quenching agent, absorbing the energy of the positive ions before they reach the cathode.

The time taken by positive ins to move away from the anode (reducing the shielding effect) so that the field comes to normal is called dead time.

This method is not suitable for detection of gamma radiations due to its low ionization effect.

BACKGROUND RADIATION

Sometimes even in the absence of a radioactive source nearby, a GM tube may still register some radiations. This is called background radiation and it is present within the atmosphere. The count registered in the absence of the radioactive substance or source is called background count. Some of the causes of background radiation include;

Cosmic rays from outer space
Radiations from the sun
Some rocks which contain traces of radioactive material, e.g., granite
Natural and artificial radioisotopes

ARTIFICIAL RADIOACTIVITY

Some naturally occurring nuclides which are not radioactive can be made artificially radioactive by bombarding nuclei of stable atoms with alpha-particles, beta-particles, protons or neutrons.

For example, when nitrogen-14( ) nuclide, which is stable, is bombarded with fast moving alpha particles, radioactive oxygen is formed. This is represented by;

+ +

Other artificially radioactive nuclides are silicon-27 ( ), sulphur-35 ( ) and chlorine-36 ( ).

THE DECAY LAW

A radioactive decay is a spontaneous, random process in which one cannot point out the nuclide that will disintegrate next. The choice of the nuclide that decays is governed by chance. This is because extremely large number of atoms is usually involved.

The decay law states that the rate of disintegration at any given time is directly proportional to the number of nuclides present at that time (remaining undecayed). This can be expressed as;

α-N; where N is the number of nuclides present at the given time. It follows that;

=-λN, where λ- is the decay constant.

Note that the negative sign indicates that the number N is decreasing with time.

is referred to as the activity of the material.

HALF LIFE

This is the time taken for half the number of nuclides initially present in a given radioactive sample to decay.

Consider 2g of radium, whose half-life is 1600 years. In 1600 years 1g will have decayed. In the next 1600 years, ½ g of the sample will be remaining. This is illustrated in the table below:

No. of years	No. of half-lives	Mass decayed (g)	Mass remaining (g)
0	0	0	2
1600	1	1	1
3200	2	1 ½	½
4800	3	1 ¾	¼
6400	4	1 7/8	1/8

It can also be shown that the number of nuclides remaining undecayed, N after time T is given by;

N = N₀(½)^T/t ; where N₀ is the original number of nuclides and t the halt-life.

A graph of the number of nuclides remaining N against time T appears as shown below:

N₀

Number

Of radiation

nuclei

0t_½ Time T

In order to plot the correct graph, it is advisable to first subtract the background radiation if does exist from each count rate before plotting the values. This will ensure that only count rate due to the radioactive material is used to plot the graph. This is because the value of the background radiation usually fluctuates.

The graph shows that the activity decreases by the same fraction in succession equal time intervals, that is, its exponential curve.

Example 5

A radioactive substance is found to have an activity of 360 counts per second. 30minutes later, it was 45counts per second. Determine its half life.

SOLN

360 t_½ 180 t_½ 90 t_½ 45

Hence ; 3t_½=30minutes

t_½=30/3 =10minutes.

Alternatively ;

N =N₀(½)^T/t½

45 =360(½)^30/t½

2^-3=2^-30/t½

-3 =-30/t^½

t_½=-30/-3 =10minutes

Example 6

A radioactive substance has a half life of 10hours. Calculate the percentage of the sample that remains after 25hours.

SOLN

N = N₀(½)^25/10

But percentage of the sample remaining after 25hrs is given by;

[N/N0] x 100

Hence; Percentage remaining = [{N₀(½)^25/10}/N₀] x 100

= 17.68%

Example 7

A GM tube is used to measure the decay of a certain radioactive substance and the results are as shown in the table below. The background radiation is 25counts per hour.

Time (hrs)	0	1	2	3	4	5
Countrate (counts/h)	425	255	175	105	73	51

Plot a graph of Countrate against time and use it to determine the half life of the material.

Example 8

When the values in the table below are plotted, we obtain the graph shown below;

The following are also common graphs that can be obtained from activity of the radioactive substances;

NUCLEAR FUSION AND FISSION

Nuclear fusion is defined as the fusing of the nuclei to form a heavier nucleus. Nuclear fusion is where light nuclei combine to form a heavier nucleus. The process is accompanied by the release of large amounts of energy. Example is the fusion of lithium and hydrogen to give helium.

+ +

Beryllium formed is radioactive hence it disintegrates into two alpha particles.

Nuclear fission is the splitting of the radioactive nuclei into more stable nuclei. Nuclear fission occurs when a nucleus splits into smaller more stable nuclei. This happens by the nucleus absorbing a neutron. During nuclear fission, the binding energy is released. Example is the fission of uranium- 235;

+ + + 2( )

The produced neutrons are called fission neutrons. One neutron may sometimes split to produce many atoms. When this occurs, it is called a chain reaction. Nuclear fission is the principle on which hydrogen bombs work. This process if not controlled may lead to explosions.

APPLICATIONS OF RADIOACTIVITY

In medicine:

Gamma rays can be used to control cancerous growths in the human body. The radiations kill cancer cells when the tumour is subjected to it.
Gamma rays are also used to sterilize surgical equipment.
It can also be used for killing pests or making them sterile.
Can also used to monitor blood circulation disorders and the functioning of thyroid gland.

In carbon dating– it uses the ratio of carbon-12 to carbon-14 to estimate the ages of fossils.
Detecting Pipe Bursts-underground pipes carrying water or oil many suffer bursts or leakages. Therefore, the content being transported through the pipe is mixed with some radioactive substance which can be detected by a radiation detector on the ground around the area of leakage.
In Agriculture– a radiation detector can be used to monitor the uptake of minerals introduced to plants by mixing it with some weak radioactive substance. Gamma rays can also be used to kill pests or make them sterile.
Determination of thicknesses of thin metal sheets, paper or plastics– a GM tube is used to measure the thickness of the metal plates, paper or plastic. The source of radiation is placed on one side while the GM tube is placed on the opposite side. The metal plate is passed between the source and the detector. The count rate registered is a measure of the thickness of the metal plate. To be more efficient, a thickness gauge can be adapted which automatically controls the thickness of the metal foils, paper or plastics. A thickness gauge can be adapted for automatic control of the manufacturing process.
Detection of Flaws– cracks and airspaces in the welded joints can be detected using gamma radiation from cobalt-60.

HAZARDS OF RADIOACTIVITY AND THEIR REMEDY

The effects of radiation on a human body depend on:

The nature of the radiation,
Dosage and
Part of the body irradiated.

Excessive exposure of body cells to radiations can lead to burn effects or genetic damage. Extreme heavy doses can be fatal. There could also be delayed effects such as cancer, leukemia and hereditary defects.

Gamma rays and beta radiation are more dangerous compared to alpha radiation due to their high degree of penetration.

PRECAUTIONS

Precautions should therefore be taken when handling radioactive materials. These include:

Always use forceps to handle radioactive materials. Never use bare hands to hold such materials.
Keep radioactive materials in thick lead boxes.
Use radiation absorbers in hospitals and research laboratories.
Reduce time spent near radiation sources.

Radioactivity

(a) Define radioactive decay

(b) A radioactive element decays to ¹/₁₂₈ of its original activity after 49 days. Determine its

half –life

238 y

U Z + 4β

92 x

(b) (i) Determine the value of x and y in the nuclear equation below:-

(ii) The half life of a radioactive element is 20minutes. The mass of the element after 120

minutes is 0.03125g. Determine the original mass of the element

(iii) What evidence supports the fact that gamma rays are not charged

(iv) Alpha particles have low penetrating power as opposed to beta particles. Give a reason

for this

v) A manufacturer wishes to check the thickness of steel sheets he produces. Explain how

this can be done using a radioactive source and a counter

a) What is meant by radio active decay?
b) Uranium 235 was bombarded with a neutron and fission took place in the following manner:

²³⁵

⁹⁰

₉₂U + ¹₀n ₃₈Rn + _bX + 10( ₀n)

Determine the values of a and b

c) When carrying out experiments with radio active substance one is instructed that the source

should never held with bare hands but with forceps. Give a reason for the instruction

d) The diagram below shows the paths taken by three radiations A, B and C from a radio

active isotope through an electric field

i) State the charge on plate Y
ii) Identify the radiation A and C

iii) Give a reason why C deviates move A

²³³

e) Th disintergrates into radium (Ra) by emission of two alpha and two beta particles as

in equation ₉₀ Th _ZRa + 2( ₂H) + 2 ( _-1)

State:

i) The atomic number of the daughter nuclide
ii) The mass number of the daughter nuclide
f) One of the application of Beta emission (B) is controlling thickness gauge. Explain

how they are used for this purpose?

The following is a nuclear reaction for a fusion process resulting from the reaction of polonium

210 S T

81 3 ßdecay 84 a decay 82

with loss of beta particles

P 1

(i) Determine the values of S and T

(ii) State the source of the energy released

The expression below is an equation for radioactive element A. Element B and C are the daughter

nuclides. A, B and C are not the actual symbols of any of the elements

238 234 X

A B + C

92 90 Y

(a) State what type of radioactive decay this is.

(b) What is the value of:

X……………… Y……………………

Arrange the following in order of increasing frequency: Red light, Infrared radiation, X-rays,

UV radiation, Short –radio waves, TV and Fm radio waves, Am radio waves and Long radio

waves.

Radium -222 is a radioactive element with a half-life period of 38 sec. What fraction of the mass

of a sample of this element remain after 380 sec.

(a) Define the term half-life of a radioactive material

(b) (i) Use the table below to plot a graph of activity against time

Activity (Disintegration/seconds)	680	567	474	395	276	160	112	64
Time t (days)	0	1	2	3	5	8	10	14

(ii) Find the half-life of the material in days

has 8 x 10¹⁰ un-decayed nuclei at time t = 0. How many un-decayed nuclei will

be left after 690 days?

(d) An element x (uranium) decays by emitting two alpha particles and a beta particle

to yield element Y

(i) State the atomic number and mass number of Y

(ii) Write down the decay equation

a) What is meant by radioactive decay?
b) A radioactive source placed 12cm from the detector produced a constant count rate

of 5 counts per minute. When the source is moved close to 3cm, the count rate varies

as follows;

Time	0	20	40	60	80
Count rate	101	65	43	29	21

i) State the type of radiation emitted.
ii) Explain the constant count rate when the source is 12cm away.

iii) Plot a graph of count rate against time (Use graph paper)

iv) Use the graph to estimate the half life of the element
State one advantage of:
i) A lead-acid accumulative over a dry cell
ii) A dry cell over lead-acid accumulator

ANSWERS

a) Radioactive decay is the spontaneous random emission of particles from the nucleus

of an unstable nuclide

(b) There are 7 half lives ( t_½ )

7t_½ = 49 days

t_½ = 49

= 7days

(b) (i) y =238-4(1) = 242

X = g2

(ii) 120 = 6 half lives

0.03125 x 26 = 2g

(iii) They are deflected by both electric and magnetic fields

(iv) Alpha particles are heavy (massive)

(v) – The sheets are brought in turns between radioactive source and the counter.

– The count rate is a measure of the thickness of the metal sheet.

a) Spontaneous disintegration of unstable atoms in order to gain stability
b) i) a = 236 – 91= 145
ii) b = 92- 38 = 54
c) radioactive substances are harmful to the body when ingested
d) i) Negative

ii)A – Beta radiation C – Alpha radiation

iii) C – more massive than A

e) i) A = 233 – 8 = 225
ii) Z = 90 – [(2 x2) + (2x – 1)]

= 90 – (4 – 2)

= 90 – 2 = 88

f) – a beta source is placed on one side of a moving sheet of paper and a G.N detector

on the other side

– If the material is too thin, the count rate at the detector will be too high and

vice versa

P 1

(i) S – 210

P 1

T – 206

(ii) The splitting of a heavy nuclide to lighter particles (fission process)

State what type of radioactive decay this is. – Alpha decay
a) X…4 Y…2
Long radio waves, AM radio waves, T.V and FM Radio waves, short Radio waves, infra red

radiation, red-light , Uv radiation and X-rays.

No. of half lifes = 380 = 10

¹/_t

N = N_o (½ )

380 = (½)¹⁰ = 1

38 1024

(a) Time taken for the activity of a sample of a radioactive material to reduce to half

of the original value

(b) (i) S – scale – simple and uniform / consistent

p – Plotting at least 4 points correct

C – Line must pass through at least 3 points

(ii) -Half-life 319 ±0.1 days (1mk)

-Readings –off from the graph clearly

(c)

Time

Nuclei

P(1mk)

8 x 10¹⁰

138

4 x 10¹⁰

276

2 x 10¹⁰

414

1 x 10¹⁰

552

0.5 x 10¹⁰

690

0.25 x 10¹⁰

Therefore Nuclei remaining un-decayed

^T/_t= 2.5x 10⁹ (1mk)

OR N = No (½ )^½

N = 8×10¹⁰(½)

= 0.25 x 1010 = 2.5 x 10⁹ (2mks)

(d) (i) mass number = 228 a.m.u (1mk)

Atomic number = 89 a.m.u (1mk)

236 232 228 228

92 90 88 96

-1

(ii)