GCSEScienceWJECScience (Double Award)PhysicsExam QuestionsForces, Space & RadioactivityHalf-Life

Half-Life (WJEC GCSE Science (Double Award): Physics): Exam Questions

Exam code: 3430

1 hour6 questions

3 marks

Pupils in a class were given 200 coins to use in an experiment to simulate radioactive decay.

They were asked to shake the coins in a bag, throw them out on the table then remove those showing “heads”. The number removed were counted and recorded in a table.

The remainder of the coins were put back in the bag and the process was repeated again and again.

Their results are shown in the table below.

Throw number	Total number of coins removed	Number of coins remaining
0	0	200
1	104	96
2	149	51
3	..........	26
4	..........	20
5	..........	6
6	..........	4

(i) Complete the table.

[1]

(ii) After two throws, the number of coins remaining was 51. How many coins would you have expected to remain?

[1]

(iii) After how many throws would the number of remaining coins fall to about one eighth of the original number?

[1]

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2 marks

Carbon-14 is a radioactive form of carbon that is present in all living material. Each nucleus of carbon-14 undergoes radioactive decay by emitting a beta particle to form nitrogen-14 according to the following decay equation, which is incomplete.

${}_{6}^{14}C \to {}_{\dots}^{\dots}N + {}_{- 1}^{0}e$

Complete the nuclear equation above.

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5 marks

A sample of 800 million carbon nuclei decays to create nuclei of nitrogen.

The decrease in the sample creates an increase in the number of nuclei of nitrogen according to the following graph.

Graph of number of carbon and nitrogen nuclei (millions) against time in thousand years, showing nitrogen curve rising and levelling near 800 million, carbon as scattered crosses

(i) Complete the following table.

[2]

Time (thousand years)	Total number of nuclei (million)	Number of nitrogen nuclei (million)	Number of carbon nuclei (million)
0	800	0	800
5	..........	360	440
10	..........	560	240
15	..........	670	..........
20	..........	730	..........
25	..........	760	..........
30	..........	780	..........
35	..........	790	..........

(ii) On the grid opposite, plot points showing the decay of the carbon-14 nuclei. The first three crosses showing the numbers of carbon nuclei have been plotted for you.

Draw a suitable line.

[3]

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3 marks

(i) State the meaning of “the half-life” of a radioactive substance.

[2]

(ii) Use the graph to determine the half-life of carbon-14.

[1]

Half-life = .......... thousand years

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2 marks

Carbon dating is used to find the age of some ancient objects because carbon-14 is present in all once-living material. The process has been used to identify the age of the Turin shroud. This is a sheet of cloth that was claimed to be about 2 000 years old. Three independent radiocarbon dating tests, carried out recently, attempted to identify the age of the cloth.

Faded monochrome image of a bearded man’s solemn face, front-facing, emerging ghostlike from a dark, textured background

Out of 80 million carbon-14 nuclei which were present in each sample of the original cloth, around 6 million have decayed into nitrogen. Use this information to explain whether the claim about its age is correct.

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2 marks

Radioactive isotopes decay at different rates.

The decay rate depends on the half-life of a particular radioisotope and the number of radioactive atoms remaining.

State what is meant by the term half-life.

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3 marks

The decay of a radioactive isotope can be modelled using 60 cubes.

Each cube has one face shaded black.

These cubes are called 1F cubes.

Scattered yellow and black 3D cubes on a grey gradient background, creating an abstract geometric pattern across the image

Describe the method used to collect results to find the half-life.

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6 marks

In a class experiment, 12 groups of students are each given 60 of these 1F cubes.

The table below shows the results from one group and for the entire class.

Throw	Number of 1F cubes remaining
Throw	For the group	For the class
0	60	720
1	50	600
2	42	500
3	36	420
4	29	350
5	24	290

(i) The results of all the groups were added to give a class result.

State why the class result is used to plot a graph and not just the result for one group.

[1]

(ii) The class repeats the experiment with different cubes.

The 2F cubes have two faces shaded black and the 3F cubes have three faces shaded black.

The class results are shown below.

Throw	Number of cubes remaining in the class
Throw	For 2F cubes	For 3F cubes
0	720	720
1	480	360
2	320	180
3	210	90
4	144	45
5	95	23

The class results for 1F, 2F and 3F cubes are plotted on the grid below.

Line graph with three decreasing curves (1F, 2F, 3F) showing number of cubes remaining from 700 to 0 over five throws, each curve dropping more steeply.

I. Add lines to the graph to determine the half-life of the 2F cubes.

[2]

half-life =..........................throws

II. Use the information in the graphs or tables to tick (✓) the boxes next to the three correct statements.

[3]

1F cubes show decay at the slowest rate $box enclose space space space space space space end enclose$

2F cubes show decay at the quickest rate $box enclose space space space space space space end enclose$

3F cubes show the equivalent of two half-lives after 2 throws $box enclose space space space space space space end enclose$

3F cubes have the longest half-life $box enclose space space space space space space end enclose$

1F cubes could also have been replaced with 720 coins and the number of heads counted after each throw $box enclose space space space space space space end enclose$

The number of 2F cubes remaining after 4 throws is about $\frac{1}{5}$ of the original $box enclose space space space space space space end enclose$

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3 marks

Sodium-24 is a radioactive isotope with a half-life of 15 hours.

A solution containing 48.0 mg of sodium-24 was injected into a patient for a medical investigation.

Calculate the mass of sodium-24 that will be left after 75 hours.

mass =......................mg

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More Revision Notes you might like

Number of throws	Number of dice remaining
0	500
1	435
2	380
3	335
4	291
5	256
6	224
7	196
8	171

Radioactive isotope	Radiation emitted	Half-life	Use
sodium-24	beta and gamma	15 hours	detecting leaks in underground pipes
technetium-99m	gamma	6 hours	radioactive tracer injected into blood
iridium-192	gamma	74 days	detecting cracks inside steel plates
francium-223	alpha or beta	22 minutes	no uses
palladium-103	beta	17 days	treating tumours by direct injection
radon-222	alpha	3.8 days	early warning for earthquakes

Fraction remaining	Time
Fraction remaining	Palladium-103	Sodium-24	Technetium-99m
1	0	0	0
$\frac{1}{2}$	17 days	15 hours	..........................
$\frac{1}{4}$	34 days	30 hours	............................
$\frac{1}{8}$	51 days	45 hours	............................
$\frac{1}{16}$	68 days	..........................	...........................
$\frac{1}{32}$	85 days	75 hours	..........................