![1
PHY 4822L (Advanced Laboratory):
Analysis of a bubble chamber picture
Introduction
In this experiment you will study a reaction between
“elementary particles” by analyzing their
tracks in a bubble chamber. Such particles are everywhere
around us [1,2]. Apart from the standard
matter particles proton, neutron and electron, hundreds of other
particles have been found [3,4],
produced in cosmic ray interactions in the atmosphere or by
accelerators. Hundreds of charged
particles traverse our bodies per second, and some will damage
our DNA, one of the reasons for the
necessity of a sophisticated DNA repair mechanism in the cell.
2
Figure 1: Photograph of the interaction between a high-energy
π--meson from the Berkeley
Bevatron accelerator and a proton in a liquid hydrogen bubble
chamber, which produces two neutral](https://image.slidesharecdn.com/1phy4822ladvancedlaboratoryanalysisofabu-221129184948-3bf5a2b0/85/1phy-4822l-advanced-laboratory-analysis-of-a-budocx-1-320.jpg)
![short-lived particles Λ0 and K0 which decay into charged
particles a bit further.
Figure 2: illustration of the interaction, and identification of
bubble trails and variables to be
measured in the photograph in Figures 3 and 4.
The data for this experiment is in the form of a bubble chamber
photograph which shows bubble
tracks made by elementary particles as they traverse liquid
hydrogen. In the experiment under
study, a beam of low-energy negative pions (π- beam) hits a
hydrogen target in a bubble chamber.
A bubble chamber [5] is essentially a container with a liquid
kept just below its boiling point (T=20
K for hydrogen). A piston allows expanding the inside volume,
thus lowering the pressure inside
the bubblechamber. When the beam particles enter the
detector a piston slightly decompresses the
liquid so it becomes "super-critical'' and starts boiling, and
bubbles form, first at the ionization
trails left by the charged particles traversing the liquid.
The reaction shown in Figure 1 shows the production of a pair
of neutral particles (that do not leave
a ionized trail in their wake), which after a short while decay
into pairs of charged particles:
π - + p → Λo + Ko,](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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- 1. 1 PHY 4822L (Advanced Laboratory): Analysis of a bubble chamber picture Introduction In this experiment you will study a reaction between “elementary particles” by analyzing their tracks in a bubble chamber. Such particles are everywhere around us [1,2]. Apart from the standard matter particles proton, neutron and electron, hundreds of other particles have been found [3,4], produced in cosmic ray interactions in the atmosphere or by accelerators. Hundreds of charged particles traverse our bodies per second, and some will damage our DNA, one of the reasons for the necessity of a sophisticated DNA repair mechanism in the cell. 2 Figure 1: Photograph of the interaction between a high-energy π--meson from the Berkeley Bevatron accelerator and a proton in a liquid hydrogen bubble chamber, which produces two neutral
- 2. short-lived particles Λ0 and K0 which decay into charged particles a bit further. Figure 2: illustration of the interaction, and identification of bubble trails and variables to be measured in the photograph in Figures 3 and 4. The data for this experiment is in the form of a bubble chamber photograph which shows bubble tracks made by elementary particles as they traverse liquid hydrogen. In the experiment under study, a beam of low-energy negative pions (π- beam) hits a hydrogen target in a bubble chamber. A bubble chamber [5] is essentially a container with a liquid kept just below its boiling point (T=20 K for hydrogen). A piston allows expanding the inside volume, thus lowering the pressure inside the bubblechamber. When the beam particles enter the detector a piston slightly decompresses the liquid so it becomes "super-critical'' and starts boiling, and bubbles form, first at the ionization trails left by the charged particles traversing the liquid. The reaction shown in Figure 1 shows the production of a pair of neutral particles (that do not leave a ionized trail in their wake), which after a short while decay into pairs of charged particles: π - + p → Λo + Ko,
- 3. 3 where the neutral particles Λo and Ko decay as follows: Λo → p + π-, Ko → π+ + π-. In this experiment, we assume the masses of the proton (mp = 938.3 MeV/c2) and the pions (mπ+ = mπ- = 139.4 MeV/c2) to be known precisely, and we will determine the masses of the Λ0 and the K0, also in these mass energy units. Momentum measurement In order to “reconstruct” the interaction completely, one uses the conservation laws of (relativistic) momentum and energy, plus the knowledge of the initial pion beam parameters (mass and momentum). In order to measure momenta of the produced charged particles, the bubble chamber is located inside a magnet that bends the charged particles in helical paths. The 1.5 T magnetic field is directed up out of the photograph. The momentum p of each particle is directly proportional to the radius of curvature R, which in turn can be calculated from a measurement of the “chord length” L and sagitta s as: r = [L2/(8s)] + [s/2] , Note that the above is strictly true only if all momenta are perfectly in the plane of the photograph;
- 4. in actual experiments stereo photographs of the interaction are taken so that a reconstruction in all three dimensions can be done. The interaction in this photograph was specially selected for its planarity. In the reproduced photograph the actual radius of curvature R of the track in the bubble chamber is multiplied by the magnification factor g, r = gR. For the reproduction in Figure 3, g = height of photograph (in mm) divided by 173 mm. The momentum p of the particles is proportional to their radius of curvature R in the chamber. To derive this relationship for relativistic particles we begin with Newton's law in the form: F = dp/dt = e v×B (Lorentz force). Here the momentum (p) is the relativistic momentum m v γ, where the relativistic γ-factor is defined in the usual way γ = [√(1- v 2/c2)]-1. Thus, because the speed v is constant: F = dp/dt = d(mvγ)/dt = mγ dv/dt = mγ (v2/R)(-r) = e v B (-r) , where r is the unit vector in the radial direction. Division by v on both sides of the last equality finally yields: mγv /R = p /R = e B ,
- 5. identical to the non-relativistic result! In “particle physics units” we find: p c (in eV) = c R B , (1) 4 thus p (in MeV/c) = 2.998•108 R B •10-6 = 300 R (in m) B (in T) Measurement of angles Draw straight lines from the point of primary interaction to the points where the Λ0 and the K0 decay. Extend the lines beyond the decay vertices. Draw tangents to the four decay product tracks at the two vertices. (Take care drawing these tangents, as doing it carelessly is a source of large errors.) Use a protractor to measure the angles of the decay product tracks relative to the parent directions (use Fig. 3 or 4 for measurements and Fig. 2 for definitions). Note: You can achieve much better precision if you use graphics software to make the measurements, rather than ruler and protractor on paper. Examples of suitable programs are GIMP or GoogleSketchUp, both of which can be obtained for free. Analysis
- 6. The laws of relativistic kinematics relevant to this calculation are written below. We use the subscripts zero, plus, and minus to refer to the charges of the decaying particles and the decay products. p+sinθ+ = p-sinθ- (2) p0 = p+cosθ+ + p-cosθ- (3) E0 = E+ + E-, where E+ = √(p+2c2 + m+2c4) , and E- = √(p-2c2 + m- 2c4) m0c2 = √(E02 - p02c2) Note that there is a redundancy here. That is, if p+, p-, θ+, and θ- are all known, equation (2) is not needed to find m0. In our two-dimensional case we have two equations (2 and 3), and only one unknown quantity m0, and the system is over-determined. This is fortunate, because sometimes (as here) one of the four measured quantities will have a large experimental error. When this is the case, it is usually advantageous to use only three of the variables and to use equation (2) to calculate the fourth. Alternatively, one may use the over-determination to "fit'' m0, which allows to determine it
- 7. more precisely. A. K0 decay 1. Measure three of the quantities r+, r-, θ+, and θ-. Omit the one which you believe would introduce the largest experimental error if used to determine mK. Estimate the uncertainty of your measurements. 2. Use the magnification factor g to calculate the actual radii R and equation (1) to calculate the momenta (in MeV/c) of one or both pions. 3. Use the equations above to determine the rest mass (in MeV/c2) of the Ko. 4. Estimate the error in your result from the errors in the measured quantities. 5. 5 Β. Λo decay: 1. The proton track is too straight to be well measured in curvature. Note that θ+ is small and difficult to measure, and the value of mΛ is quite sensitive to this measurement. Measure θ+, r- and θ-. Estimate the uncertainty on your measurements. 2. Calculate mΛ and its error the same way as for the Ko. 3. Estimate the error in your result from the errors in the
- 8. measured quantities. 4. Finally, compare your values with the accepted mass values (the world average) [3], and discuss. C. Lifetimes: Measure the distance traveled by both neutral particles and calculate their speed from their momenta, and hence determine the lifetimes, both in the laboratory, and in their own rest-frames. Compare the latter with the accepted values [3]. Estimate the probability of finding a lifetime value equal or larger than the one you found. References: [1] G.D. Coughlan and J.E. Dodd: “The ideas of particle physics”, Cambridge Univ. Press, Cambridge 1991 [2] “The Particle Adventure”, http://particleadventure.org/ [3] Review of Particle Physics, by the Particle Data Group, Physics Letters B 592, 1-1109 (2004) (latest edition available on WWW: http://pdg.lbl.gov ) [4] Kenneth Krane: Modern Physics, 2nd ed.; John Wiley & Sons, New York 1996 [5] see, e.g. K. Kleinknecht: “Detectors for Particle Radiation”, Cambridge University Press, Cambridge 1986;
- 9. R. Fernow: “Introduction to Experimental Particle Physics”, Cambridge University Press, Cambridge 1986; W. Leo: Techniques for Nuclear and Particle Physics Experiments : A How-To Approach; Springer Verlag, New York 1994 (2nd ed.) Note: Experiment adapted from PHY 251 lab at SUNY at Stony Brook (Michael Rijssenbeek) 6 Figure 3 : Photograph of the interaction between a high-energy π--meson from the Berkeley Bevatron accelerator and a proton in a liquid hydrogen bubble chamber. The interaction produces two neutral particles Λ0 and K0, which are short-lived and decay into charged particles a bit further. The photo covers an area (H•W) of 173 mm • 138 mm of the bubble chamber. In this enlargement, the magnification factor g = (height (in mm) of the photograph )/173 mm.
- 10. 7 Fig. 4: Negative of picture shown in Fig. 3 HIGHER COLLEGE OF TECHNOLOGY DEPARTMENT: BUSINESS STUDIES Final Examination: Assignment Based Assessment Semester: II A. Y.: 2019 / 2020 Diploma I and II Year Start Date: 16-5-2020 Time: 9:00AM Due Date: 18-5-2020 Time: 9:00AM Student Name Student ID Specialization Section
- 11. Level Diploma I –Year Course Name Principles of Microeconomics Course Code BAEC1203 For official Use Only Question No. Max. Marks Obtained Marks Question No. Max. Marks Obtained Marks 1 5 1 5 2 5 2 5 3 5 3 5 4 5 4 5 5 5 5 5 6 5 6 5 7 5 7 5 8 5 8 5 9 5 9 5 10 5 10 5 Grand Total Marks 50 50
- 12. First Marker: Second Marker: Date: Date: Guidelines for Students to Submit the Assignment: 1) The final assessment for semester 2, 2019-20 will be done through comprehensive assignment for a maximum of 50 marks. The schedule of the final assessment is available in the college website. https://www.hct.edu.om/about/the- college/announcements/final-assessment-timetable-041620 2) All the students are expected to have only one assignment at one time. In case, if the students have more than one assignment on the same day, please report to the exam committee through the following mail id. [email protected] as soon as possible. 3) All students are given 48 hours to complete and submit each assignment from the day, date and time the assignment is uploaded. Students are advised not to wait till the last moment of the deadline to submit the assignment. 4) The students can check the assignment anytime and any
- 13. number of times from the opening of the assignment. The answer to the assignment need to be uploaded in e- learning within 48 hours. 5) The answer to the assignment can be uploaded only one time. No requests for resubmission of the assignment will be entertained. 6) In case students face any difficulties while uploading the assignment in e-learning, they can contact ETC helpdesk. For Academic related support : Business Courses For Technical Writing 1 For Technical Writing 2 For Technical Communication [email protected][email protected][email protected][email prote cted][email protected] For issues related to e-mail accounts and Microsoft Teams [email protected] Any issues related to E-Learning Moodle [email protected]
- 14. Any other IT Troubleshooting [email protected] 7) Student may contact their respective lecturer through email (within the 48-hour period given) if they have any doubts and clarifications on the assignments. 8) Student should be aware that this assignment is an independent assessment. Students are not allowed to get help from any other person during the assessment period. 9) Students assignment will be checked for plagiarism through Turnitin software. This assignment will be assessed as per the College Assessment Policy. Student will be investigated in case of plagiarism as per the College policy and procedures. 10) In case the students face any technical issues regarding the submission of assignment, the answer to the assignment can be mailed to the concerned lecturer within the 48- hour period. 11) Any assignment submitted after the 48-hour period will not be considered for evaluation.
- 15. 12) The assignment should be submitted only the file in MS Word document. No other format is acceptable at all (e.g. pictures, JPEG, PDF, etc.) 13) The students need to answer the assignment in the prescribed number of words as mentioned in the assignment. 14) The students need to follow the following format while preparing the assignment : Font Style: Times New Roman Font Size: 12 point for body and 14 point for Headings Line Spacing: 1.5 Margin: 2.54cm (One inch) on all the sides Page Number: At the bottom right hand corner of each page Colour: All words should be in black colour 15) Students who will fail to submit their assignment as per the deadline given are required to make an online appeal along with the valid excuses as the guidelines which will be announced through the college website or e- learning portal.
- 16. Main Instructions: 16) At the time of answer papers submission in the E-Learning, Students have to follow the two things importantly: i) When you are submitting the answer paper through e- learning, Students have to delete all instructions points from the answer sheet (1-16) (Guidelines for Students to Submit the Assignment): ii) When you are submitting the answer sheet, delete questions from the answer sheet. Mention question numbers with the answers. These are the above two instructions, students have to be followed strictly. Then only it will show less plagiarism percentage, if students are not followed, it shown more plagiarism, due to that you marks may be low. All the Best
- 17. CASE STUDIES (Suggested time: 48 hours) Answer all the questions given below the case studies. For every question given, it should be answered with minimum fifty hundred (50) words and maximum hundred (100) words per question. Part-I Food delivery is the present trend nowadays especially that most people are required to stay home. In the case of Patsy restaurant, the company has effectively operated in Oman for many years catering to non-Omani and Omani foods. With the required take-out and home delivery only, the restaurant has to reduce the workforce. Some of the Cooks were separated and one of them is Zara’s father. The family has stayed in Oman living comfortably. Her family enjoys their wealth by spending on different luxury products. Now that the father loses his job, the family started to live on their remaining limited resources.
- 18. Q1 What concept/s can best describe the situation and how can the family survive their present condition. (5 Marks) _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________
- 20. _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ____________________ Part-II Zara’s family did not lose hope. The father can either look for another restaurant for employment or partner with other friends to start a homemade cooked food delivery. But before they decided on this business, the group conducted a study to finally make a choice of a new venture. Now their problem is to choose which business will continue to support their families. Q2 Explain the five problems that must be faced (or) dealt with before attempting to start the business. (5 Marks)
- 23. ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ Q3 Describe the opportunity cost of each choice whether to apply for another job or put up a business. Defining Opportunity cost 2.5 Marks+ answer related to case 2.5 Marks) _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________
- 25. _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ Part-III In order to assure success, the new business has to consider the demand and supply situations in Oman. The new delivery business may face competition with similar business but offering other type of food (Asian, Indian, Arabic dishes). Now that
- 26. there is a lockdown, the supply of some of the materials needed may not be available in the market. Further, some homes are also extra careful in ordering food and would rather cook their own in their kitchen. The new business will also have to prove that they are practicing safety measures to assure customers that their food is safe. They found out that the present virus situation has led to shortage of protective items like masks and gloves. Q4 Explain five factors that can specifically affect the increase and decrease in the demand for the homemade food delivery. (5 Marks) _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________
- 28. _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ Q5 Explain five factors that can specifically affect the supply of these items that are needed by the new business. (5 Marks) _____________________________________________________ ______________________ _____________________________________________________
- 31. _____________________________________________________ ______________________ Part-IV When the business was launched, initially they offered eight (8) types of meat dishes, vegetable dishes and seafood. There are also desserts and sandwiches. Knowing that they have competition with another homemade food delivery company, the business lowered its price from 5 RO to 3 RO per dish. Likewise, the number of dishes was increased to ten (10). Q6 What kind of elasticity is being shown here? Calculate the elasticity. (5 Marks) _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________
- 34. In order to minimize costs, the business uses a vacant room in one of the partners’ house to store the products. The business is also being run by members of the family like their wives and Zara and the other children. They deliver the products to the different shops using their own van. They deliver the products to the different shops using their own van. Power and Wi-Fi per month cost the business 400 RO. Raw materials which are the ingredients for the food costs 250 RO per week. Petrol is about 60 RO per month. Repairs and maintenance of the van costs 30 per month. Salaries in the form of allowances to the two Helpers cost 35 RO each per month. Profit for the first month was 3000 RO and during the second month it increased to 5,000 RO. Q7 Solve for the firm’s: 1) fixed cost; 2) average fixed cost; 3) average variable cost; 4) average total cost and 5) marginal revenue for the first and second month. (5 Marks) _____________________________________________________ ______________________
- 37. ______________________ Q8 Describe the explicit and implicit costs in this situation. (5 Marks) _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________
- 39. _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ Part- VI Putting in mind the situational demands for their homemade foods, the business relates with their customers on a daily basis. The business keep tract of the market prices and the news related to the operation of the business. Zara being a college graduate is a big help to the business. She gives feedback and suggest strategies to her father and the partners. Now they are concentrating only on specific dishes per day but since she is aware of the competition,
- 40. the business will try to keep operating. There may be seasons that the business may just break even and they are expecting this. Q9 What kind of market structure is being described here and what other characteristics does this market structure show. (5 Marks) _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________
- 42. _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ _____________________________________________________ ______________________ Q10 What will the business do in the following situation 1) When the prices in the market is higher than equilibrium price. (2.5 Marks) 2) When there is shortage of demand. (2.5 Marks) _____________________________________________________ ______________________ _____________________________________________________
- 58. average is � = !! ! = 17. Next find (�! − �)! Then � = (!!!!)! ! !!! !!! = 2.21 To calculating standard uncertainty u when a set of
- 62. 1 2 (�!! + �!!) Where �!! ��� �!! are initial and final momentums of Σ particle. And can be found using the measured track length �!. The length of time that the Σ−lives(the time
- 63. between its creation and decay) is � = �! � ���������� ������ �� ���� �� �ℎ� ��� � = �! � 1 − �! �! ���������� ������ ������ ���ℎ �������� � = �!�! �!�