Assignment 10
Radioactive decay and space
Introduction
Aims
This assignment will test your ability to:
? answer multiple-choice questions
? describe practical situations and interpret measurements.
You do not need to have studied the physics that underlies these experiments in order to be able to complete the tasks.
Links to the assessment requirements
The assessment objectives for the A level that are relevant to this assignment are to:
? apply knowledge and understanding of scientific ideas, processes, techniques and procedures: ? in a practical context
? when handling qualitative data
? when handling quantitative data
? analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to:
? make judgements and reach conclusions
? develop and refine practical design and procedures.
How your tutor will mark your work
Your tutor will assess the following aspects of your work:
? your application of appropriate physical principles
? your use of appropriate equations
? the accuracy of your calculations
? your use of graphs and drawings where directed ? your use of appropriate units.
Are you ready to do this assignment?
Before you tackle this assignment, ensure that you have studied Section 10 of the course and Chapters 9, 13 and 14 of the textbook.
In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler and protractor, graph paper and a calculator.
The assignment
In calculations, use g = 9.81 m s–2 for the acceleration of free fall unless told otherwise. Data for other questions can be found in the Data booklet, which is linked to Section 6.
1 A nucleus decays by first emitting a beta particle, followed by an alpha particle, and then a second beta particle. You can say the following about the remaining element:
(a) It is an isotope of a new element.
(b) It is an isotope of the original element.
(c) It has the same number of nucleons as it had at the start.
(d) It has more nucleons than it had at the start.
(1 mark)
2 In radioactive decay, which of these is the best description of the decay constant ??
(a) The rate of decay of the isotope.
(b) The constant that links the rate of decay to the half-life.
(c) The constant that links the rate of decay to the number of undecayed nuclei.
(d) The reciprocal of the half-life of the isotope.
(1 mark)
3 What is the nearest equivalent of 1020 m?
(a) 1.06 ? 104 light years
(b) 2.54 ? 105 light years
(c) 6.36 ? 105 light years
(d) 3.87 ? 106 light years
(1 mark)
4 If a distant galaxy is moving away from us we will observe that the light reaching us has: (a) a higher frequency
(b) the same frequency
(c) a shorter wavelength
(d) a longer wavelength.
(1 mark)
5 The measurements in Table 1 were made on a radioactive substance with a short half-life.
Table 1 Data for Question 5
Time/min Count rate
C/s–1 Time/min Count rate
C/s–1
0 1620 7.0 234
0.5 1347 7.5 218
1.0 1223 8.0 186
2.0 883 9.0 126
3.0 715 10.0 112
4.0 547 11.0 81
5.0 417 12.0 79
6.0 315 13.0 53
(a) Plot a graph, using linear scales, of count rate versus time
(having converted to seconds). Draw a best-fit curve through
the points and make at least three measurements to estimate the half-life of the isotope.
(5 marks)
(b) This type of graph always has scatter. What is the most likely
reason? Explain your answer.
(2 marks)
(c) Plot a graph of ln C versus time. Find the decay constant from the plot, and use this to calculate the half-life of the isotope.
(5 marks)
6 Discuss the nature, penetration through materials and ionising ability of alpha, beta and gamma radiation. With particular reference to the penetration through materials, discuss the effect of these radiations being incident on the surface of a
human. (6 marks)
7
(a) Explain what is meant by binding energy.
(2 marks) (b) Using the graph in Figure 1, calculate an approximate total
binding energy for a nucleus of .
(2 marks)
Figure 1 Graph for Question 7
(c) For the following nuclear reaction, calculate the energy released:
The data required are in Table 2 (other constants are in the data sheet).
Table 2 Data for Question 7
Mass/u
Neutron 1.008665
Uranium-235 235.0439
Molybdenum-95 94.9058
Lanthanum-139 138.9061
(3 marks)
8
(a) Proxima Centauri is the closest star to the Earth. Figure 2 shows the measurements made from the Earth on its travel around the sun.
Figure 2 Diagram for Question 8 (not to scale)
The angle ? is 0.762 seconds of arc, and the radius of the orbit of the Earth around the sun is 1.5 ? 1011 m. Calculate
the distance to Proxima Centauri, marked d in the diagram, in m.
(3 marks)
(b) Describe in your own words what is meant by a standard candle, and how they can be used to measure distances to stars that are too far away to have a measurable parallax.
(3 marks)
9
(a) Our sun has a wavelength of maximum intensity of emission approximately 510 nm. Use Wien’s law to estimate its surface
temperature in Kelvin, to two significant figures. (Note that
the data you need are in the data sheet.)
(3 marks)
(b) Using the Stefan–Boltzmann law, and given that the luminosity of the sun is 3.9 ? 1026 W, calculate the radius of the sun, giving your answer to two significant figures.
(3 marks) (c) The radiation from the sun can be represented as Figure 3:
Figure 3 Diagram for Question 9 (not to scale)
Sketch this diagram and add a curve for a star that has a
surface temperature lower than the sun.
(2 marks)
(d) The distance from the sun to the Earth is 1.50 ? 1011 m (to three significant figures). Calculate the radiation flux received from the sun (neglecting any effect from the atmosphere). Give your answer to two significant figures.
(3 marks)
10
(a) Sketch a Hertzsprung–Russell diagram, showing the positions of the main sequence, white dwarfs, red giants and supergiants. There is no need to use colour.
(6 marks)
(b) Mark on your diagram the path of a star from its early ‘proto-
star’ stage until it joins the main sequence.
(2 marks)
11 A line from the hydrogen spectrum from a distant galaxy is observed at 700 nm, where it should be 486 nm.
(a) Calculate the red-shift and the approximate velocity of the
galaxy, relative to our galaxy.
(4 marks)
(b) If the Hubble constant is 2.3 ? 10–18 s–1, calculate the approximate distance of the galaxy. You will find the equations you need on the data sheet.
(2 marks)
Total for assignment 60 marks
Submit your assignment
When you have completed your assignment, submit it to your tutor for marking. Please use pdf format. Your tutor will send you helpful feedback and advice to help you progress through the course.