Consider the fig below  
Whereby;  
•
1T1/2 = First half life,  
2T1/2 =Second half life  
and 3T1/2 =Third half life period  
Example  
1. From the figure below determine the half life  
4. Isotope has a half-life of 1min and 1000 nuclei initially present, after 1min will decay to 500  
nuclei, next 1min will decay to 250 nuclei, and next 1min will decay to 125 nuclei and so on  
Graphically  
Written by Geoffrey M Idebe (0688 082 089)  
Page 73  
NB:  
o
Half-life is the same for isotope  
o
o
Half-life is independent to physical state, temperature and pressure  
Radioactive isotope never decay to zero value  
Individual task – 3:3  
1. A sample of a radioactive contains 120 nuclei. Calculate the number of half-life it  
takes for the sample to decay so that there are only 15 nuclei left undecayed (ANS: n =3)  
2. What is the half life of a radioactive material if its activity falls to 1/8 of its value  
in 3360 seconds  
3. The half-life of iodine-131 is 8 days. A sample contains 800g of iodine-131.  
How much of the sample will remaining undecayed after 40 days (ANS: 25 g  
4. The half-life of iodine-131 is 8 days. A sample contains 16g of iodine-131  
(a) Draw a graph to represents  
)
(b) From the graph determine mass of the sample which will remain  
undecayed after 20 days  
5. Archaeologist can determine the age of organic matter by measuring the  
proportion of carbon -14 present in a sample. Assuming that carbon -14 has a  
half –life of 5600 years ,Calculate the age of a piece of wood found to contain  
1/8 as much carbon -14 as in a living material (ANS: t = 16 800 yrs  
)
6. Explain why long half –life of nuclear waste products presents a health hazard  
(
ANS:  
If the half –life is long/large, the activity remains at a very high level for a  
very long time resulting in a health hazard)  
7. A radioactive isotope  
M
decays by emitting two alpha and beta particles to form  
ퟐퟏퟒ풀  
.
What is the atomic number of  
M
. After 224 days, 1/16 of mass of  
M
ퟖퟑ  
remained. Determine the half life of  
M
.(ANS: Atomic number = 87, t1/2 = 56 days)  
Detection of Nuclear Radiations  
•
Nuclear radiation is detected by its ability of ionizing the atom/molecules of gas  
passed through the detector, we have about many devices but the first-three  
are the common detectors includes  
Written by Geoffrey M Idebe (0688 082 089)  
Page 74  
(a) Geiger Muller tube (GM tube)  
(b) Spark counter  
(c) Cloud chamber  
(d) Photographic plate (film)  
(e) Bubble chamber  
(f) Gold leaf electroscope  
Geiger Muller Tube  
•
Is a device which detects radiations by ionization of noble gas such as argon in  
a closed tube  
Composition of Gm Tube  
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✓
Hollow tube consists of noble gas (argon) coated metallic film maintained at a  
high negative voltage relative to the collector  
Mica thin window at one end where radiation allowed passing through mica  
during detection  
A collector wire at the centre of tube  
Mechanism of Gm Tube  
•
When radiation enters the tube, it causes electrons to be ejected from the  
gaseous atoms and are then accelerated toward the positively–charged  
collector wire  
•
•
Then an electron strikes the wire causing a brief pulse of electric current to be  
produced  
Finally the current can cause a ‘’click’’ in a speaker or be counted by a scalar  
Background radiation  
•
•
Is the natural radiation that is always present in the environment  
It comes from (sources) the earth’s crust, the atmosphere, cosmic rays and  
radioisotopes  
Background Count Rate  
•
Are the radiations present in the environment even when there is no apparent  
radioactive material around  
OR  
OR  
Is the number of counts recorded by a radiation detector from background radiation  
Is the evidence or effect on a detector of radiation caused by background radiation  
Written by Geoffrey M Idebe (0688 082 089)  
Page 75  
Source of Background Count Rate  
•
•
•
Earth’s radioactive impurities  
Residue of nuclear radiation present in G.M.T  
Cosmic rays escape from outer space through ozone layer  
NB  
:
•
A GM tube left well away from a radioactive source will still count some  
radioactive emissions (The background count).  
•
•
•
•
If the GM tube is placed close to a radioactive source, it will count the  
emissions from the source and the background count  
Background radiation count must be subtracted from the total count registered  
by a detector to obtain the actual /correct count of the source  
Example if the background was 5 Bq and the count recorded is 45 Bq, then the  
count from the source is ( 45 – 5 = 40 Bq)  
In calculations the Background count rate is treated as zero. i.e. not allowed (it  
is subtracted from recorded count rate)  
Individual task – 3:4  
1. The activity of a radioactive element when measured using the Geiger Muller  
tube was found to be 63 counts per minute. Given that the background  
radiation was 8 counts per minute, determine  
(a) The actual activity of the radioactive element (Actual Activity = 63 – 8=55 c.p.m)  
(b) The half –life of the element if the activity dropped from 128  
counts/minute to 23 counts per minute in 6 hours (ANS: t = 2hrs)  
2. In an experiment to determine the half –life of the radioactive element, the  
following data was obtained.  
Activity (counts) per minute  
52 44 34  
28.5 24  
19.0 17.5 15  
Time (minutes)  
0
0.5 1.0 1.5  
2.0 2.5  
3.0  
3.5  
(a) Given that the background radiation is 10 counts per minute, Plot a  
decay curve for the element  
(b) Estimate from your graph, the half –life of the element (t1/2 = 1.15 minutes)  
3.  
A Geiger Muller tube connected to rate meter is hold near a radioactive source, the  
corrected count rate(allowing for Background count rate is 400 c.p.s. 40 min the  
corrected count rate is 25c.p.s. What is the half-life of the source? (ANS t1/2 = 10 min)  
4. A rate meter records a background count rate of 2 c.p.s, when a radioactive  
source is held near the count rate is 162 c.p.s. if the half-life of the source is 5  
min. what will the recorded count rate be 20 min? (ANS N = 10 c.p.s)  
Written by Geoffrey M Idebe (0688 082 089)  
Page 76  
Spark Counter  
•
Spark counter is the device used to detect the presence of radiation based on  
their ability to ionize dry air molecules by producing sparks  
Diagram  
Composition of Spark Counter  
➢
➢
➢
Piece of wire gauze  
Long wire  
Power supply with voltage below level required to cause a spark  
Mechanism of Spark Counter  
•
When radiation pass through dry air cause dry air to ionize which increases  
conductivity of dry air allowing electrons to pass through them to form sparks  
NB  
:
The number of sparks produced depends on the types of radiation emitted  
✓
✓
✓
When Alpha (  
produced due to highest ionization effect  
When Beta (β) particles are emitted the least number of sparks are produced  
due to moderate ionization effect  
훼
) particles are emitted the largest number of sparks are  
When Gamma (γ) rays are emitted the few number of sparks are produced due  
to lowest ionization effect  
Wilson Cloud Chamber  
•
•
Is a device used to detect presence of radiation by producing tracks of light  
It is sealed environment containing a supersaturated vapour of water, alcohol  
or any other compound that can be kept near its condensation point by  
regulating the temperature of the chamber. Supersaturated vapour of water  
refers to a vapour of a compound (water) that has a higher (partial) pressure  
than the vapour pressure of that compound (water).  
Written by Geoffrey M Idebe (0688 082 089)  
Page 77  
Composition of Cloud Chamber  
✓
✓
✓
✓
✓
✓
✓
Felt ring soaked in alcohol: to supply alcohol vapour to the chamber  
Radioactive source: produce radiation and cause ionization of vapour  
Dry ice: uses to cool the alcohol vapour until it is saturated  
Alcohol vapor condensation: to form liquid droplets around the ionized molecule  
Lamp: uses to light track which cause to view it clear  
Foam: support dry ice  
Plastic lid: the eyepiece  
Mechanism of Cloud Chamber  
•
•
•
The air inside chamber is ionized by the radiation in its path.  
This leads to the formation of air ions  
Alcohol vapor condenses on these air ions forming droplets along the path ie  
forms some tracks  
•
•
These droplets/tracks are visible and so radiation is detected  
Each radiation forms a definite pattern. The radiation is identified by analyzing  
the nature of the pattern formed  
Individual task – 3:5  
A snap shot photograph of a cloud chamber shows 40 tracks well defined alpha  
particle track. A second snap shot taken 2 min later shows only 10 tracks. What is the  
half-life of the alpha source?  
(
ANS: T1/2 = 1 min  
)
Photographic Film  
•
Radiation exposes the film  
Bubble Chamber  
•
It is similar to a cloud chamber but bubbles are formed in a liquid along the  
path of the radiation. It detect alpha and beta particles  
Gold Leaf Electroscope  
•
Charged leaf of the electroscope collapses when a radioactive source is  
brought nearby. Then the air surrounding the leaves become ionized, the  
charge on the leaf can “leak” away  
Advantage of diffusion cloud chamber detector over charged electroscope  
•
It can detect alpha, beta and gamma radiations unlike a charged electroscope  
which can only detect alpha particles  
Written by Geoffrey M Idebe (0688 082 089)  
Page 78  
Difference between X-Rays and Gamma Rays  
❖
❖
❖
❖
x-rays are caused by energy transition in electron while gamma rays are  
caused by nuclear reaction within the nuclear  
metal (e.g. tungsten) used to produce x-rays not decaying while metal used to  
produce gamma rays decaying  
Wavelength of x-rays determined by nature of target and operating voltage  
while gamma rays depending on the nuclear for their wavelength  
X-rays are emitted by stable atoms of heavy nucleus while gamma rays  
formed nucleus of energetically unstable to became stable  
Class Activity – 3  
1. A patient suffering from cancer of thyroid glands is given a dose of radioactive  
iodine 131, with a half-life of 8 days, to combat diseases. He is temporarily  
radioactive and his nurse must be changed regularly to project them. If his  
radiation is initially 4 times the acceptable level, how long is it before the special  
nursing radiations can be dropped (ANS : t = 16 days)  
2. The half life of iodine – 131 is 8 days .A sample contains 16 g of iodine – 131  
(a) Draw a graph to represent the decay of the sample  
(b) From the graph determine mass of the sample which will remain undecayed  
after 20 days (ANS: (a) Draw graph (b) 3g)  
3. A sample contains 800 g of iodine – 131.How much of the sample will remain  
undecayed after 40 days ? (The half life of iodine – 131 is 8 days) (ANS: 25 g)  
4. Isotope A has a half – life of 36 s and decays by emission of alpha particle to  
Isotope B . Isotope B has a half life of 18 s and decays by emission of beta  
particle to isotope C which is stable .A sample initially contains 120 mg of pure  
Isotope A. After 72 s :  
(a) What mass of Isotope A remains?  
(b) What mass of Isotope B has been produced?  
(c) Of the mass of Isotope B produced, how much remains?  
(d) What mass of Isotope C has been produced?  
(e) After which of the following times would there be less than 1 mg of isotope  
A remaining? ((a) 120 s  
(b) 160 s (c) 240 s  
(d) 280 s)  
5. The half life of Technetium 99m is 6h. If 12 mg of Technetium 99m is injected into  
a patient and starts to decay into Technetium 99m .Calculate the amount of  
Technetium 99m present in the patient after 24h  
ANS:  
6. After 24 days, 2 mg of an original 128 mg sample remain .What is the half – life of  
the sample?  
(ANS: 4 days)  
7. U – 238 has a half life of 4.46 x 109 years .How much U – 238 should be present  
in a sample 2.5 x 109 years old .If 2 g was present initially ? (ANS: 1.36 g remain)  
8. How long will it take for a 40 g sample of I–131 (Half – life = 8.04 days) to decay to  
1/100 its original mass?(ANS 53.4 days)  
Written by Geoffrey M Idebe (0688 082 089)  
Page 79