500 778 333 500 444 1000 500 500 333 1000 556 333 889 778 611 778 tube from the lead castle and attach it horizontally to a stand provided. Course Hero is not sponsored or endorsed by any college or university. MODERN PHYSICS . Three times as great? 9.l>T[hiHi?IExZ:A)M3U3-L~| Pakistan Institute of Engineering & Applied Sciences, Islamabad, 245504425-LAB-3-Radiation-Heat-Trasfer.docx, 193656_RISHITENA_AL_UMAPATHI_._THERMAL_RADIATION_LAB_REPORT_1399701_2129133553.docx, Effect MS df F p p STAI Y1Time 56410 2 903 0001 0258 Time x Condition 12996, Chapter 5 Subqueries 51 Noncorrelated Subqueries 52 In Line Views Objectives, 744EE09A-EAB5-4503-A13F-C6C4E87E4DA1.jpeg, A well meant policy that has had clear unintended consequences for instance is, Week 1- Calculating Productivity exercise.docx, Which of the following conditions is one of the consequences of congestive heart, Module 4_ Lesson 2 - Knowledge Check_ Ethical Hacking - 61424.pdf, Bristol v Board of Cty Commrs 312 F3d 1213 10th Cir 2002 A county boards budget, minimizes encroachment upon adjoining traffic lanes promotes speed uniformity, References 1 Milou Feijt Yvonne de Kort Inge Bongers Joyce Bierbooms Joyce, Are the events A B and C mutually independent 550 You roll a fair die once, Advanced_Assessment__Interpreting_Findings_and_Formulating_Differential_4E__1_.pdf-678.pdf, Which side e ff ect would the nurse assess for when caring for a patient on, Hi, I would really appreciate if someone could show me step by step answers to these problems that I've been stuck on for a long time. We have learned that radiation travels in all direction in straight lines from the center of the source like rays from the Sun. (Radiation spreads . Inverse Square Law of Gamma Radiation Experiment, https://www.imagesco.com/nuclear-science/geiger-counter/experiment-4.html, Testing the Inverse Square Law for Gamma Radiation, We've added a "Necessary cookies only" option to the cookie consent popup. The intensity of radio waves over distance obeys the inverse-square law, which states that intensity is inversely proportional to the square of the distance from a source. " E! By hTPn0[dt4NwE1%$8 :7{ae#W`[Wt :GZ; Place beta radiation source into hole on wooden block of rail tracker. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Look at the inverse square law with a source (pick a strong one) with no shielding. An Improvement to the Inverse Square Law Light Experiment Richard Borne (Northern Illinois University) has suggested an improvement to the Inverse Square Law Light Experiment using our [name oek] (order code OEK). The source is not a point source. No, because the wrist-watch glass is small and all the legs of the spherometer cannot rest on it. Jordan's line about intimate parties in The Great Gatsby? He noticed that the intensity of our white LED lamp decreases somewhat over time when it is first turned on. 417 14
They have low penetrating power. ;.d3X:^t60`"D>"bMHe yw~fS'||9G-$|_x1 Move Geiger counter and slider to 16 cm from the source. Basic experiment in nuclear physics Make the other connections as shown in the Fig. Sometimes these approximations are good, sometimes they are not. How can I make this regulator output 2.8 V or 1.5 V? If a source has an intensity, The current Occupational Safety and Health Administration (OSHA) ceiling limit for H 2 S is up to 20 ppm for general industry. Beta particles are electrons. Next place an aluminum shield of approximately 1/8 (4mm) thickness in-between the source and gm tube. -:Hv3tDbJ$8 :#
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8.1.7 Required Practical: Inverse Square-Law for Gamma Radiation. A Geiger counter measures the number of radioactive particles that hits it in a period of time. Geiger counter is also called as G.M. 0
MathJax reference. What happens to the intensity of beta activity when the distance between the Geiger counter and source is four times as great as the initial distance? The polonium-210 has a half-life of 138 days. 722 722 722 722 722 722 722 564 722 722 722 722 722 722 556 500 Place the counter on the slider, 8 cm from the beta source. is there a chinese version of ex. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 =u!U%CUvI@{/s]F`t.a%pyh$Xgj4s m{N.68%G~g (G//:^ +nA~Bh*Lnj$EMFYW.eYzjrK Cm
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Verification of Inverse Square Law using G.M. In three dimensions, the density of something leaving a . Counter 761 views Jul 21, 2021 This is an experiment to verify inverse square law. Equipment per student/group Notes on equipment gamma ray source and handling tools GM tube and counter These could be connected to a datalogger but total count must be displayed. Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. The diameter, Basically, says is that if you move to a distance d away from the window of the GM, counter, then the intensity of radiation decreases by a factor. Dead time refers to the time taken by the tube to recover between counts. In this experiment the distances are 8 cm, 16 cm, 24 cm, and 32 cm from the source. > . I have collected data and the graph comes out looking right. If you took background CPM reading and subtracted them from every distance reading do you think the red line would cross closer to zero? 2 0 obj Using the shields and your knowledge of shielding identify the "mystery" source. <<8ea7d6289a1d294e826d5e8acdda051b>]>>
h+x5~T5 mj`%`0 ;n!d~'U3]fc~xtSm7v9 |NTs=^9;/5&gq%]i#hn{nlgy*9I~,(~rvyEe;S&u{4;Lr!o'{k|Ly{j?v=?9zm.P?)gI!YxhO}|oG3o("'>m:?*#e?5bqkedaH>\QO!qnx.Z~9z_ a/=l/aszoL:c`9Flmkyb.q- +VXC>5. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. % /AwCU9Z7w~U|h(HrvbDNAO? T{-. Hence, the source bloc is shifted in 2 cm steps from 20 cm up to 40 cm. Since students doing this experiment may take a few minutes to collect . Determine the uncertainty in the gradient of the graph. Use this information to graph your results. I place this source 4 cm from the front of the GM tube. A Geiger-Mller counter is used to detect the radiation intensity at distances of 2, 3, and 4 meters. I am conducting an experiment in which I investigate the relationship between the counts per second detected by a Geiger Counter and the distance between said Geiger Counter and the source of radiation. 90 0 obj
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The absorption of the radiation by the air could explain the observed deviation from the inverse square law. To verify inverse square law of radiation using a photoelectric cell fIf L is the luminous intensity of an electric lamp and E is the illuminiscence (intensity of illumination) at point r from it, then according to inverse square law. Would the background activity be the same taken at sea level as taken on top of a mountain? %|?&g ah"*+9Y^>mccH!Y7}a^t@+"Z4Z/w
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Record the calculation in column 8 of the Data Table. The inverse square law is thus verified. The diamagnetic susceptibility for tap water obtained is 7.87x10 6. 0000000576 00000 n
600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 Move Geiger counter to 24 cm and repeat step 6. Introducing a constant k and rearranging gives. In this experiment, we will examine each type of radiation using a Geiger counter and verify it penetrating power using paper, aluminum and lead shields. -1!o7!
' %PDF-1.4 2. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. Graph the activity readings (cpm) vs. 1/r. The law states that the, intensity of radiation is inversely proportional to the square of the distance from the, source. 419 0 obj<>stream
EXPLAIN. The inverse square law may not seem to hold over the full range of N's. It is exactly what Coulomb's law tells us. 0000007877 00000 n
Q.10: What will be the effect of: . 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 The first source we will use is the polonium-210 alpha particle source. Physics Practical viva-voce Questions-2019 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 It requires about 200 s for the tube to recover. Record your results. stream I placed this source 3 cm from the front of the GM tube. In this experiment, we will examine the Inverse Square Law. Spin and parity transition levels gamma radiation, Beta decay kinetic energy affecting resultant gamma-ray angle. 333 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 Record your results. The divergence of a vector field which is the resultant of radial inverse-square law fields with respect to one or more sources is proportional to the strength of the local sources, and hence zero outside sources. The inverse-square law is articulated as: I 1 I 2 d 2 2 d 1 2 Where the intensity of light is measured by candela or Lumen, and the distance is measured in meters. Carefully remove the plastic protective cap from the end of the Nuclear Sensor. The inverse square law of distance is demonstrated with the gamma radiation from a 60-Co preparation, the half-value thickness and absorption coefficient of various materials determined with the narrow beam system and the corresponding mass attenuation coefficient calculated. When Experiments using Geiger Muller Counter (GM) a. Objectives. Newton's law of universal gravitation follows an inverse-square law, as do the effects of electric, light, sound, and radiation . Has 90% of ice around Antarctica disappeared in less than a decade? The error in locating the source can be eliminated by using the procedure and analysis described in Testing the Inverse Square Law for Gamma Radiation. The Inverse Square Law dictates that we scale the irradiance from the surface of the Sun by a factor of , or 2.155 10 5. Most beta radiation can be blocked by 1/8 (4mm) of aluminum. The irradiance estimated at the Sun's photosphere is 6.33 10 7 W/m 2. At 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 To explore and calculate (if any) the relationship between the distance from radioactive sources and the intensity of beta radiation. 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 778 I started measuring CPM counts at 16 centimeters from the source using the side of the GM tube. Take CPM readings as before. If you were supplied with a radioactive sample, could you determine the percentages of alpha, beta and gamma radiation being emitted from the source. Verification of inverse square law using GM counter assembly. . Next place a lead shield of approximately 1/8 (4mm) thickness in-between the source and GM tube. In this experiment, we will examine each type of radiation using a Geiger counter and verify it penetrating power using paper, aluminum and lead shields. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 What is the meaning of the x-intercept? It will need to be in close proximity to the mica window. Thank you so much.. B. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. . Oscilloscope Absorber Foil Kit containing 10 lead absorbers from 800 to 8000 mg/cm2 and 20 aluminum absorbers from 0 to 3000 mg/cm2 Stand for GM Counter; contains GM Tube and stand with 6 counting levels Purpose The purpose of this experiment is to familiarize the student with the Geiger-Mueller counter. [ 13 0 obj This is the quantitative relationship between the irradiance (surface brightness) of light and the distance from a point source. Homework Statement. signing in and out, not leaving them unattended, warning notice on the door. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 Hamilton 09/07/2022. Procedure Place beta radiation source into hole on wooden block of rail tracker. 1. Why does the impeller of torque converter sit behind the turbine? Gravitation, light, sound, and electricity also follow. Calculate the uncertainty as the square root of the number of counts. are in use. We classify this ionizing radiation into three major categories; gamma rays, beta and alpha particles. Efficiency of GM counter for various sources b. TESTS OF THE GRAVITATIONAL INVERSE-SQUARE LAW | Annual Review of Nuclear and Particle Science 0 Skip to content For Librarians & Agents For Authors Inverse Square Law Experiment In this experiment we will examine the Inverse Square Law. xWOSW>{GH%u@|lh?l[:+UHsudc?lIB3Hshoy}yOo P @Jx1
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1.2.3 Determining Uncertainties from Graphs, 2.2.7 Collaborative Efforts in Particle Physics, 2.3 Conservation Laws & Particle Interactions, 2.4.2 Threshold Frequency & Work Function, 3.2.4 Required Practical: Investigating Stationary Waves, 3.3.4 Developing Theories of EM Radiation, 3.3.5 Required Practical: Young's Slit Experiment & Diffraction Gratings, 4.3.7 Required Practical: Determination of g, 4.6.2 Area Under a Force-Displacement Graph, 4.6.5 Kinetic & Gravitational Potential Energy, 4.8.2 Required Practical: The Young Modulus, 5.2.4 Required Practical: Investigating Resistivity, 5.4 Electromotive Force & Internal Resistance, 5.4.1 Electromotive Force & Internal Resistance, 5.4.2 Required Practical: Investigating EMF & Internal Resistance, 6.2.1 Conditions for Simple Harmonic Motion, 6.2.3 Calculating Maximum Speed & Acceleration, 6.2.8 Required Practical: Investigating SHM, 6.5.5 Avogadro, Molar Gas & Boltzmann Constant, 6.5.6 Required Practical: Investigating Gas Laws, 7.1.5 Gravitational Field Strength in a Radial Field, 7.2.2 Calculating Gravitational Potential, 7.2.3 Graphical Representation of Gravitational Potential, 7.3.1 Circular Orbits in Gravitational Fields, 7.4.7 Comparing Gravitational & Electrostatic Forces, 7.5.2 Graphical Representation of Electric Potential, 7.7.4 Required Practical: Charging & Discharging Capacitors, 7.8.1 Magnetic Force on a Current-Carrying Conductor, 7.8.6 Required Practical: Investigating Magnetic Fields in Wires, 7.9.3 Principles of Electromagnetic Induction, 7.9.6 Required Practical: Investigating Flux Linkage on a Search Coil, 8.1.4 Inverse-Square Law of Gamma Radiation, Measure the background radiation using a Geiger Muller tube without the gamma source in the room, take several readings and find an average, Next, put the gamma source at a set starting distance (e.g. ?{SnTh/*83T?Ze(IX^a8:"T|fU4S}^>V|%oKa*BR_5h|jxu4Bzbr}a
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Record counts per minute (cpm) in Table 1.1 for each trial and calculate the average. Next place a lead shield of approximately 1/2 (13mm) thickness in-between the source and GM tube. Once the table is filled, perform the calculations; d2, 1/d2. /Filter /FlateDecode %PDF-1.4
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The purpose of this lab is to introduce students to the inverse square law. Hence this ndicates the verification of the equations derived and method devised. Notice the red line doesnt go through all the plotted points. I was watching a video on YouTube the other day and it showed the inside of a green bean picker. View LAB NO.4.pdf from PHYSICS 1 at Sana'a University. Explain how distance and radioactive materials are potential hazards to you. You will need an alpha, beta and gamma button sources. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 The aim of this experiment is to verify the inverse square law for gamma radiation of a known gamma-emitting source Variables Independent variable = the count rate / activity of the source, C Dependent variable = the distance between the source and detector, x (m) Control variables The time interval of each measurement Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, How to calculate gamma radiation shielding? 39 0 obj
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The further the detector is from the sealed source the better the approximation is that it is a point source although the type of source you are likely to be using will be very small in dimension, $\approx$ 1 mm. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. endstream
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Inverse square law formula is used in finding distance or intensity of any given radiation. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. The inverse square law equation allows a direct calculation of the intensity of radiation at a predetermined distance from the source. Is a hot staple gun good enough for interior switch repair? Think of it this way: double the distance, and you get four times less power. Mller in 1928, and are used to detect radioactive particles ( and ) and rays ( and x). E! Harm from gamma radiation compared to beta radiation. Presented By : Shivani Malvi B.Sc. [CDATA[ (d) Verification of Inverse Square Law Remove the G.M. ,BO:|AP%hiBhR feNH >d* Mjo
A student measures the background radiation count in a laboratory and obtains the following readings:The student is trying to verify the inverse square law of gamma radiation on a sample of Radium-226. An Easy Inverse Square Law Rule of Thumb. Do your data calculations agree with the inverse square? crop production prediction github. COUNTER. The law states that the intensity of radiation is inversely proportional to the square of the distance from the source. To obtain accuracy for this experiment the distance between the source and the detector (GM tube) needs to be several times greater than the diameter of the GM tube. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 How to react to a students panic attack in an oral exam? . endstream
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As the source is sealed there might be an error associated as to locating the precise position of the source so a greater distance between the source and the detector will reduce the error produced by not knowing precisely where the source is located. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 hTPn 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 3s|MVdw~@ QW3-K YuIFz=hWC U&ei-Q:F3~G-aS.|=I3L'Aj Once the results are graphed, it should resemble the graph provided below. << Use the reflection plane, goniometer and microwave transmitter and receiver to verify Equation 1, the Law of Reflection. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 The inverse-square law works as follows: If you double the distance between subject and light source, it illuminates a surface area four times greater than the one before. As the area of the light sensor is constant the light sensor reading can be taken as the . Post author: Post published: February 3, 2022 Post category: fairfax high school special education Post comments: construction ventures construction ventures U'C3/ZzQ;B$FX8"a#(z1Yn{!/QaDS7QoGjO"=(;*wu'ZG0WHc7H/$oYI>)nM\`?)(ZBdhcb Hq @cDfKC&Rej=
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,:PI{sBqO|o(`U>(*o0 To begin, take five or more background CPM measurements, and record the results. Deviations from the inverse square law have been sought in three ways: The law has been checked in the laboratory over distances up to about 1 metre. This law, called an inverse-square law, is based purely on geometry: we live in three spatial dimensions, and therefore the inverse-square law holds. & Press the bell icon for latest update. Okb]B*lv|{nZrypT(]OglXMm"9vs{leL+b|b.Xcm]fS3Ob`Ze~LYL# #$
[ If you want subjects to be evenly lit from one side to the other, crank up the power and make the distance of the flash no less than the width of your subject . Setting it up: The Co-60 sources are stored in the "radiation closet" of the Physics 191 lab. Next use the Sr-90 beta source. endobj verification of inverse square law using gm counter experiment. 4.3. 9 0 obj The Geiger-Mller Counter Geiger-Mller (GM) counters were invented by H. Geiger and E.W. The "inverse square law" applies to geometric dilution of radiation around a source in the limits of point approximations for the source and detector, negligible material attenuation between source and detector, and no scattering. When performing this experiment with a cup source and GM Tube it says that you should start at a distance several times the diameter of the GM tube in order to obtain accurate results ( https://www.imagesco.com/nuclear-science/geiger-counter/experiment-4.html ). Abstract We review recent experimental tests of the gravitational inverse-square law and the wide variety of theoretical considerations that suggest the law may break down in experimentally acces. ] What are some tools or methods I can purchase to trace a water leak? A suitable table of results might look like this: According to the inverse square law, the intensity, Intensity is proportional to the corrected count rate, C, so, Comparing this to the equation of a straight line, y = mx, Square each of the distances and subtract the background radiation from each count rate reading, Plot a graph of the corrected count rate per minute against 1/, If it is a straight line graph through the origin, this shows they are directly proportional, and the inverse square relationship is confirmed, The Geiger counter may suffer from an issue called dead time, This is when multiple counts happen simultaneously within ~100 s and the counter only registers one, This is a more common problem in older detectors, so using a more modern Geiger counter should reduce this problem, The source may not be a pure gamma emitter, To prevent any alpha or beta radiation being measured, the Geiger-Muller tube should be shielded with a sheet of 23 mm aluminium, Measure the count over the longest time span possible, A larger count helps reduce the statistical percentage uncertainty inherent in smaller readings, This is because the percentage error is proportional to the inverse-square root of the count, Reduce the exposure time by keeping it in a lead-lined box when not in use, Do not point the source at anyone and keep a large distance (as activity reduces by an inverse square law), Safety clothing such as a lab coat, gloves and goggles must be worn. Do EMC test houses typically accept copper foil in EUT? Another well-known inverse square law is Newton's Law of Gravitation. forest park school district 91 salary schedule walk behind green bean harvester for sale. 0 units (Min. 722 722 722 722 722 722 889 667 611 611 611 611 333 333 333 333 IBO was not involved in the production of, and does not endorse, the resources created by Save My Exams. endobj
&" 0 V" 7 z >&. 500 500 500 500 500 500 500 549 500 500 500 500 500 500 500 500 for any queries write down in the comment box. VI Semester Govt Autonomous PG College Chhindwara MP If you like our video, please Like, Share and Subscribe. Record your results. Record your results. Chlorine, Oxygen, Fluorine, Hydrogen Peroxide, concentrated Nitric Acid, Which organic compound with a vapor density of 2.7 produces acetic acid vapor when it interacts with water? Kerr effect -determination of Kerr constant of a Liquid 31. /Creator (easyPDF SDK 4.1) ] The data taken is also presented. Place the counter on the slider, 8 cm from the beta source. Which is why this link starts taking readings at 16cm as its many more times the diameter of the GM Tube he used. 556 722 667 556 611 722 722 944 722 722 611 333 278 333 469 500 Science Workshop Inverse Square Law - Nuclear dg 1996, PASCO scientific P60 - 3 1. Next use the Co-60 gamma source. The closer the points are to the line, the better the experiment has demonstrated the relationship. 0
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In this experiment we will examine the Inverse Square Law. The dimension formula of G is [M-1 L 3 T-2]. According to the inverse square law, when the distance is doubled from 8 cm to 16 cm the reading should decrease to 1/4 its initial reading. Step 1: Determine a mean value of background radiation, Step 2: Calculate C (corrected average count rate) and C1/2, Step 3: Plot a graph of C1/2 against x and draw a line of best fit, Step 4: Determine the uncertainties in the readings, Step 5: Plot the error bars and draw a line of worst fit, Step 6: Calculate the uncertainty in the gradient. Basically it consists of a pair of electrodes surrounded by a gas. [ 160. Genetically Modified Mosquitoes: Are They Preparation of Methylene Blue Stain. 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 That makes Coulomb's Law an example of an inverse square law. The further the better. Inverse-Square Law of Radiation. Kvl#n4q To learn more, see our tips on writing great answers. The purpose of this experiment is to find the range of gamma rays and determine if the inverse square law applies. hb```f``Jd`e`Lgb@ !+6kZ3d0d@R"x~B[YnrUP\e10Xt@f@|Fl3rR@,
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I want to create a linearised graph of the data to investigate the results . At what point of what we watch as the MCU movies the branching started? 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 The following experiment will use a completely safe beta b particle of radiation (Strontium-90). 417 0 obj <>
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Record your results. [Note: You may need to use MS Excel to record data for your graphs to answer the questions on Turntables Explore] 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 600 Place the gamma ray source at each distance mark and take five CPM readings. Researchers generally look for a new force that violates Newton's inverse-square law with a characteristic length scale: this involves looking for a potential of the form V = -(GMm/r) (1 + e -r/ ), where is a . To obtain, accuracy for this experiment, the distance between the source and the detector (GM, tube) needs to be several times greater than the diameter of the GM tube. One presentable timer with 3 digit display & thumb wheel switch. The strength of different oxidizers varies. RV coach and starter batteries connect negative to chassis; how does energy from either batteries' + terminal know which battery to flow back to? Use MathJax to format equations. How many atoms of Cobalt-60 will remain after 26.3 years if the source has 8 x 10 9 today? Q.9: Can you measure the radius of curvature of wrist-watch glass by using a spherometer? EXPERIMENT 1 Gamma-Ray Absorption and Counting Statistics Note: Please read the Radiation Safety Regulations at the back of this book Introduction The detecting medium in a scintillation counter is a solid or liquid material called a phosphor, which emits tiny ashes of light (scintillations) when struck by ionising radiations. Featured Listing. Attached in my solution is a graph of the counts per second over time. xWM6W6(Ytlm"i95=mE)7-$5y3~|Q$92I67xH\rE,/[KQ>OH~S%}d!nHvA[/LBK9m6+7gU-{mkUUeq'D.rpig&wmSEHpzB~0 A piece of work I am doing for college (UK college that is) has me investigating the inverse square law for gamma radiation. Inverse Square law: The radiation Intensity is inversely proportional to the square of the distance. A few minutes to collect ) a as its many more times the diameter of graph. 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