Investigating the Inverse Square Law Essay

The inverse determine righteousness can also be applied to gravity, electric fields, light and sound. In relation to electric fields, the electric force in Coulombs law follows the inverse squ be lawIf gamma rays are a form of electromagnetic light beam and undergo negligible absorption in air, then the intensity, I, should vary inversely as the square of the distance between the commencement and the detector.2Air acts as an almost transparent medium to ?-rays, and the intensity ( outrank of energy arrival per unit area) of ?-rays emanating from a elevation source varies inversely as the square of the distance from the source.3?-rays fall into many distinct monoenergetic groups because of their variable energies which emanate from any particular emitter. The least energetic ray will only pass finished very thin foils, whereas the most energetic can penetrate up to several centimetres of lead.4 As ?-rays tend to amaze 10-4 times as many ion-pairs per unit length as ?-particles do, legal communityments are usually carried out using a Geiger-Mller (G-M) render.5G-M resistances are widely used for find radiation and ionising particles.Source http//en.wikipedia.org/wiki/Geiger-M%C3%BCller_tubeThe anode is a central thin wire which is insulated from the surrounding cathode cylinder, which is metal or graphite coated. The anode is kept at a cocksure electromotive force and the cathode is earthed. The tube may also have a thin mica end window.6When radiation enters the tube, a few electrons and ions are produced in the gas. If the voltage is higher up the breakdown potential (The minimum reverse voltage to make the diode conduct in reverse)7 of the gas, the number of electrons and ions are greatly multiplied. The electrons are attracted to the anode, and the positive ions collide with towards the cathode. The current flowing in the high resistance resistor (R) produces a pd which is amplified and passed to a weigher which registers the passage of an io nising particle or radiation through the tube.8The tube cannot be filled with air as the discharge persists for a short time after 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 vapour which quenches, reduces the intensity, the discharge quickly, ensuring that the registered radiation does not affect the recording of some other ionising particles.When the G-M tube is discover sensation particle, if another enters the tube it will not be detected. This is known as dead time the average maximum being approximately 90 microseconds.9 Because this number is so small, it can justifiably be ignored for this experiment.Background radiation must be taken into account when taking knowledges from the source. Background radiation primarily comes from cosmic radiation and terrestrial sources.10 This radiation will affect the count and must be corrected. T he level of this radiation varies with location and must be measured before conducting the experiment.Since I ? CC ? 1(d + d0)2Therefore d + d0 ? 1VcI ? 1r2Where* d = distance* d0 = distance to be added to the measured distance, d, because of the reference point on the holder not coinciding with the source, and the effective counting space inside the GM tube may not be close to the window, then r = d + d0.* I = intensity* C = corrected count rate the measured count rate negative the reading for background radiation11Corrected count rate against 1/(d + d0)2 should produce a straight- termination graph, passing through the origin, if the inverse square law is followed.Source A Laboratory Manual of natural philosophy -F. Tyler, Page 269The gradient of the line obtained is a measure of the strength of the source used in the experiment.12 The strength of the source is the activity, A=?N. The break down constant, ?, can be calculated using ? = ln2/t1/2 where the value for the half-lif e 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 ensure the utmost safety before, during and after this experiment, some guidelines should be followed* viands and drink should not be consumed whilst in the same room as the source* Food items should not be stored in the same room as the source* The source should only be handled with long handled source handling tongs, and as little as possible* Hands should be washed good after contact 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 radial in only one direction, it should not be pointed at anyone* The source should be locked away in a lead lined box when not in use* Open wounds should be covered securely* Protective gloves should be warn when handling potentially contaminated itemsErrorsTo reduce the possib le errors deep down the experiment, an opthalmic bench will be used to ensure that the G-M tube and the source are properly aligned 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 much accuracy as possible. Vernier callipers read to fractions of a millimetre, making them much more(prenominal) accurate than other measuring devices. Other distances, such as distance d, can be measured with a metre rule as the distances are larger which decreases the possible error in measuring.There will also be the error of human reaction times from observing the final count and pressing the stopclock. To ensure accuracy, practise using the stop-clock and count switch until reasonably consistent results can be obtained.Preliminary Wo rkTo decide on an arrogate voltage to use, the G-M tube and source set-up should be tested. Place the source approximately 10 cm from the window of the G-M tube and increase the voltage slowly, until the count rate stops changing dramatically.Plot a graph of the count-rate, C, against EHT voltage, V. Record the voltages V1 and V2 between which the rate of counting does not vary too much. If the rate of counting begins to parachute after remaining much the same for a bunk of voltage do not raise the voltage any higher or the tube may suffer damage.14The optimum operating voltage will be halfway between the voltage where the plateau begins and the voltage where it ends.To decide on the range of distances used, the source was moved 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 fell to a low value, b ut could still provide adequate results (35 cm).d (cm)Nt1 (s)t2 (s)t3 (s)Ave. t5.0010,000212209209210.0010.0010,000773779790780.6715.00 thousand180220205201.6720.001000317355345339.0025.001000457469437454.3330.001000543510542531.6735.001000749720735734.67From these preliminary 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 values will take considerably longer to measure. I will take three readings from each, as radioactive decay is a random process and it would be unlikely for more than three readings to be similar. An average will be calculated from the three values and the reading for the background radiation will be subtracted to find the corrected count rate.Equipment* Geiger-Mller tube of , ? sensitive type* Decade scaler with variable EHT supply* Sealed cobalt-60 source sealed to prevent contact with the source and to prevent isotropic radiation* Long handled sou rce handling tongs to prevent contact with the source* ocular 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 dDiagramWhere* 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-60Cobalt-60 will be used as the gamma source as it is easily produced, by exposing natural cobalt to neutrons in a reactor, and therefore easy to acquire.15 It also produces ?-rays with energies of 1.17 MeV and 1.33 MeV.Method1. Clamp the G-M tube to one end of the optical bench and attach it to the input socket of the scaler2. Set the variable EHT voltage on the scaler at a minimum and turn it on, allowing a few minutes for the scaler to cordially up3. Change the variable EHT voltage on the scaler to the value found throug h 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. Place 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 repeat twice7. Move the ?-source to 10.0 cm from the window of the G-M tube and repeat procedure 5, preferably 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 until a distance of 30.0 cm is reached10. Tabulate these results and find the average count rate for each distance11. Evaluate 1/(d + do)212. Using the put down value for background radiation, evaluate the corrected count rate for each distance13. Plot the graph of corrected count rate against 1/(d + do)2Reference s1 http//hyperphysics.phy-astr.gsu.edu/Hbase/forces/isq.html2 Essential Pre-University Physics Whelan & Hodgson, page 9533 Essential Principles of Physics Whelan & Hodgson, page 4724 Essential Principles of Physics 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 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