Investigating the Inverse Square Law Essay

The inverse significant vivid law can likewise be applied to gravity, electric fields, light and sound. In relation to electric fields, the electric string in Coulombs law follows the inverse square lawIf da Gamma rays are a form of electromagnetic radioactivity and undergo negligible submersion in air, then the gaudiness, I, should vary inversely as the square of the outmatch among the germ and the detector.2Air acts as an almost transparent medium to ?-rays, and the intensity ( range of energy arrival per unit area) of ?-rays emanating from a point microbe varies inversely as the square of the distance from the spring.3?-rays fall into m all a nonher(prenominal) distinct mono ready groups beca employ up of their variable energies which emanate from any particular emitter. The least energetic radioactivity get out completely pass with very thin foils, whereas the most energetic can penet identify up to almost(prenominal) cen beattres of lead.4 As ?-rays tend to produce 10-4 time as many ion-pairs per unit space as ?-particles do, measurements are usually carried fall out using a Geiger-Mller (G-M) metro.5G-M resistances are astray utilise for notice ray of light and ionising particles. descent http//en.wikipedia.org/wiki/Geiger-M%C3%BCller_ underpassThe anode is a central thin expatriateing wire which is insulated from the surrounding cathode cylinder, which is metal or graphical recordite coated. The anode is kept at a corroborative potential and the cathode is earthed. The supply may besides have a thin mica end windowpane.6When radiation sickness enters the tube, a hardly a(prenominal) electrons and ions are produced in the gas. If the electromotive force is supra the breakdown potential (The minimum atavism potential to make the diode conduct in reverse)7 of the gas, the deed of electrons and ions are greatly multiplied. The electrons are attracted to the anode, and the positive ions move towards the cathode. The new flowing in the high fortress resistor (R) produces a pd which is amplified and passed to a take career which registers the passage of an ionising particle or radiation through the tube.8The tube cannot be modify with air as the land persists for a short time subsequently the radiation is registered. This is due to electrons being emitted from the cathode by the positive ions which arrive there. Instead, the tube is filled with argon mixed with a halogen desiccation which quenches, reduces the intensity, the discharge quickly, ensuring that the registered radiation does not impress the recording of other(a) ionising particles.When the G-M tube is detecting iodin particle, if another enters the tube it pass on not be detected. This is known as dead time the fair(a) utmost being approximately 90 microseconds.9 Because this number is so microscopical, it can justifiably be ignored for this experiment.Background radiation essential be taken into ac weigh when pickings readings from the outset. Background radiation primarily comes from cosmic radiation and terrestrial sources.10 This radiation testament affect the determine and mustiness be reverse. The level of this radiation varies with location and must be careful before conducting the experiment.Since I ? CC ? 1(d + d0)2 wherefore d + d0 ? 1VcI ? 1r2Where* d = distance* d0 = distance to be added to the measured distance, d, because of the reference point on the caster not coinciding with the source, and the efficacious number space inside the GM tube may not be close to the window, then r = d + d0.* I = intensity* C = rectify count rate the measured count rate minus the reading for cathode-ray oscilloscope radiation11Corrected count rate against 1/(d + d0)2 should produce a straight-line graph, passing through the origin, if the inverse square law is followed. line A Laboratory manual of physics -F. Tyler, Page 269The gradient of the line obtained is a measure of the strength of t he source used in the experiment.12 The strength of the source is the activity, A=?N. The decay constant, ?, can be reckon using ? = ln2/t1/2 where the value for the half life of Co-60 is 5.2714 years13.Therefore? = ln2/t1/2= 0.693/1.664 x 108= 4.175 x 10-9The gradient of the straight line graph will equal ?N0e-?t so ? = gradient/ N0e-?tSafety PrecautionsTo batten down the utmost safety before, during and after this experiment, some guidelines should be followed* Food and drink should not be consumed whilst in the same agency as the source* Food items should not be stored in the same elbow room as the source* The source should only be handled with long handled source use tongs, and as little as practicable* Hands should be washed thoroughly after touch with the source* If in contact with the source for an extended period, it is recommended that a monitoring badge is worn* As the source will radiate in only one direction, it should not be pointed at anyone* The source should be locked forward in a lead lie box when not in use* Open wounds should be covered hard* Protective gloves should be warn when discussion potentially contaminated itemsErrorsTo reduce the achievable delusions within the experiment, an opthalmic bench will be used to warrant that the G-M tube and the source are properly reorient throughout, as the source radiates in one direction, the alignment must remain standard. Also, for small distances, specifically the distance d0 which is the distance the source is from the opening of the holder plus the distance of detection from the window in the G-M tube, vernier callipers will be used to hold as a great deal accuracy as possible. vernier callipers read to fractions of a millimetre, qualification them much more accurate than other measuring devices. Other distances, such as distance d, can be measured with a metre dominate as the distances are larger which decreases the possible error in measuring.There will also be the error of human chemical reaction times from observing the final count and pressing the stopclock. To ensure accuracy, practise using the stop-clock and count switch until reasonably coherent results can be obtained.Preliminary turn overTo decide on an appropriate potentiality to use, the G-M tube and source set-up should be tested. show up the source approximately 10 cm from the window of the G-M tube and increase the electromotive force slowly, until the count rate stops ever-changing dramatically.Plot a graph of the count-rate, C, against EHT electric potential, V. go in the voltages V1 and V2 between which the rate of counting does not vary too much. If the rate of counting begins to rise after remaining much the same for a range of voltage do not raise the voltage any higher(prenominal) or the tube may suffer damage.14The optimum run voltage will be center(a) between the voltage where the plateau begins and the voltage where it ends.To decide on the range of distances used, t he source was move close to the window of the G-M tube and was moved back slowly until the scaler could count adequately (5 cm). This is the smallest distance that will be used. To find the other extreme, the source was moved back until the count rate swing to a low value, but could equable provide adequate results (35 cm).d (cm)Nt1 (s)t2 (s)t3 (s)Ave. t5.0010,000212209209210.0010.0010,000773779790780.6715.00 gram180220205201.6720.00 gibibyte317355345339.0025.00 jet457469437454.3330.001000543510542531.6735.001000749720735734.67From these approach results I have decided to time for 10,000 counts at 5 cm from the source, 5000 counts for 10cm from the source, and 1000 for 15 30cm. This is because any higher value will take considerably time-consuming to measure. I will take trine readings from each, as radioactive decay is a random process and it would be unconvincing for more than tercet readings to be similar. An average will be calculated from the three values and the readi ng for the earth radiation will be subtracted to find the corrected count rate.Equipment* Geiger-Mller tube of , ? sensitive figure* Decade scaler with variable EHT supply* close cobalt-60 source sealed to prevent contact with the source and to prevent isotropic radiation* Long handled source handling tongs to prevent contact with the source* optic bench with source holder to ensure constant alignment* Stop-clock, readable to at least two decimal places* Vernier callipers to measure the distance d0 to a higher level of accuracy* Metre rule to measure the distance dplatWhere* B is the optical bench with source holder, H* G is the Geiger-Mller tube* S is the decade scaler with variable EHT supply* R is the sealed radioactive source, cobalt-60 conscientious objector-60 will be used as the gamma source as it is easily produced, by exposing natural cobalt to neutrons in a reactor, and then easy to acquire.15 It also produces ?-rays with energies of 1.17 MeV and 1.33 MeV.Method1 . fasten the G-M tube to one end of the optical bench and attach it to the input socket of the scaler2. class the variable EHT voltage on the scaler at a minimum and turn it on, allowing a few minutes for the scaler to warm up3. Change the variable EHT voltage on the scaler to the value found through preliminary work and set it to count pulses from the G-M tube4. Start the stopclock and measure the background radiation for an adequate length of time, e.g. 25 minutes, as background radiation is variable5. mystify the holder containing the ?-source at 5.0 cm from the window of the G-M tube6. Start the stopclock and stop after 10,000 counts are registered. Record this value and absorb twice7. Move the ?-source to 10.0 cm from the window of the G-M tube and repeat surgical operation 5, instead only counting 5000 counts8. Move the ?-source to 15.0 cm from the window of the G-M tube and repeat procedure 5, instead counting only 1000 counts9. Repeat procedure 7 for sets of 5.0 cm un til a distance of 30.0 cm is reached10. put over these results and find the average count rate for each distance11. Evaluate 1/(d + do)212. Using the recorded value for background radiation, evaluate the corrected count rate for each distance13. Plot the graph of corrected count rate against 1/(d + do)2References1 http//hyperphysics.phy-astr.gsu.edu/Hbase/forces/isq.html2 Essential Pre-University natural philosophy Whelan & Hodgson, page 9533 Essential Principles of natural philosophy Whelan & Hodgson, page 4724 Essential Principles of physical science Whelan & Hodgson, page 4725 Essential Principles of physics Whelan & Hodgson, page 4726 http//www.imagesco.com/articles/geiger/03.html7 http//en.wikipedia.org/wiki/Breakdown_voltage8 Essential Pre-University Physics Whelan & Hodgson, page 4069 http//www.imagesco.com/articles/geiger/03.html10 http//en.wikipedia.org/wiki/Background_radiation11 Advanced level practical(a) Physics M Nelkon & JM Ogborn, page 21812 A Laboratory Manual of Physics F. Tyler, page 26913 http//en.wikipedia.org/wiki/Cobalt* 14 Advanced Level Practical Physics M Nelkon & JM Ogborn, page 21215 http//en.wikipedia.org/wiki/Cobalt