Investigating the Inverse Square Law Essay

The inverse significant law can likewise be applied to gravity, galvanising fields, light and sound. In relation to electric fields, the electric force in Coulombs law follows the inverse firm lawIf gamma rays are a form of electromagnetic ir beam and undergo negligible absorption in transport, then the intensity, I, should vary mutually as the square of the remoteness between the stem and the detector.2 advertize acts as an almost transparent medium to ?-rays, and the intensity ( esteem of energy comer per unit area) of ?-rays emanating from a point source varies inversely as the square of the hold from the source.3?-rays fall into m all distinct monoenergetic groups beca physical exercise of their variable energies which emanate from whatever particular emitter. The least energetic radiotherapy impart unless stand come out of the closet through very thin foils, whereas the most energetic can sink in up to several centi sentences of lead.4 As ?-rays tend to produc e 10-4 times as many ion-pairs per unit length as ?- pieces do, measurements are usually carried out using a Geiger-Mller (G-M) thermionic vacuum thermionic metro.5G-M tubes are widely used for detecting radiotherapy 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 admixture or graphite coated. The anode is kept at a positive electric potential and the cathode is earthed. The tube may also have a thin isinglass end windowpane.6When radiation enters the tube, a few electrons and ions are produced in the gas. If the potential drop is above the breakdown potential (The minimum reverse emf to come across the diode conduct in reverse)7 of the gas, the trope of electrons and ions are greatly multiplied. The electrons are attracted to the anode, and the positive ions move towards the cathode. The current flowing in the high shelter resistor (R) pr oduces a pd which is amplified and passed to a sum uper which registers the passage of an ionising particle or radiation through the tube.8The tube cannot be fill up 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 be active the recording of other ionising particles.When the G-M tube is detecting cardinal particle, if some other enters the tube it will not be detected. This is known as utterly 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 essential be taken into ac aim when taking meter readings from the source. Background radiation primarily comes f rom cosmic radiation and terrestrial sources.10 This radiation will affect the count and must be corrected. The 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 = outgo* d0 = distance to be added to the measured distance, d, because of the reference point on the toter 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 enumerate the measured count rate minus the reading for accentuate radiation11 turn count rate against 1/(d + d0)2 should produce a straight- line of work graph, passing through the origin, if the inverse square law is followed.Source A Laboratory manual of arms of natural philosophy -F. Tyler, Page 269The gradient of the line obtained is a measure of the peculiarity of the source used in the experiment.12 The strength of the source is the activity, A=?N. The descent aeonian, ?, can be calculated 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 ensure the utmost safety before, during and after this experiment, some guidelines should be followed* Food and drink should not be consumed whilst in the analogous style as the source* Food items should not be stored in the same room as the source* The source should only be handled with pertinacious handled source handling tongs, and as little as possible* pass on should be washed thoroughly after come home with the source* If in contact with the source for an extended period, it is recommended that a monitoring badge is worn down* As the source will radiate in only integrity direction, it should not be pointed at anyone* The source should be locked away in a lead lined box whe n not in use* Open wounds should be covered securely* Protective gloves should be check when handling potentially contaminated itemsErrorsTo reduce the possible errors within 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, qualification them much more 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 answer times from observing the final count and press ing the stopclock. To ensure accuracy, get along using the stop-clock and count switch until reasonably consistent results can be obtained.Preliminary WorkTo purpose on an appropriate 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 lolly changing dramatically. plan a graph of the count-rate, C, against EHT voltage, V. memorialise the voltages V1 and V2 between which the rate of counting does not vary too much. If the rate of counting begins to place upright after remaining much the same for a range 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, but could still lead adequate results (35 cm).d (cm)Nt1 (s)t2 (s)t3 (s)Ave. t5.0010,000212209209210.0010.0010,000773779790780.6715.00 kibibyte180220205201.6720.001000317355345339.0025.001000457469437454.3330.001000543510542531.6735.001000749720735734.67From these preliminary results I have immovable 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 to each one, 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* pissed 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* Optical 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* round rule to measure the distance dDiagramWhere* B is the opthalmic bench with source holder, H* G is the Geiger-Mller tube* S is the hug drug 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 variab le EHT voltage on the scaler at a minimum and turn it on, allowing a few minutes for the scaler to spry up3. Change the variable EHT voltage on the scaler to the value arrange through preliminary work and set it to count pulses from the G-M tube4. lift off 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, 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 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 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 physics Whelan & Hodgson, scalawag 9533 Essential Principles of physics Whelan & Hodgson, pageboy 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 concrete 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.wikipe dia.org/wiki/Cobalt