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Investigating the Inverse Square Law

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Introduction

Investigating the Inverse Square Law

Task:

Do gamma rays from a point source obey the inverse square law?

Planning:

Sources used in research of the above task are:

  • ‘Advanced Level Practical Physics’ – M Nelkon & JM Ogborn, pages 212 – 218
  • ‘Essential Pre-University Physics’ – Whelan & Hodgson, page 406 + 953
  • ‘Essential Principles of Physics’ – Whelan & Hodgson, pages 470 + 472
  • ‘A Laboratory Manual of Physics’ – F. Tyler, page 269
  • http://hyperphysics.phy-astr.gsu.edu/Hbase/forces/isq.html
  • http://en.wikipedia.org/wiki/Background_radiation
  • http://en.wikipedia.org/wiki/Cobalt
  • http://www.imagesco.com/articles/geiger/03.html
  • http://en.wikipedia.org/wiki/Geiger-M%C3%BCller_tube
  • http://en.wikipedia.org/wiki/Breakdown_voltage

The Inverse Square Law states that the intensity of γ-radiation diminishes as the distance from the source increases.

image03.png

Source: http://hyperphysics.phy-astr.gsu.edu/Hbase/forces/isq.html

‘The intensity of the influence at any given radius, r, is the source strength divided by the area of the sphere.’ [1]

The inverse square law can also be applied to gravity, electric fields, light and sound. In relation to electric fields, the electric force in Coulomb’s law follows the inverse square law:

image04.png

‘If gamma rays are a form of electromagnetic radiation and undergo negligible absorption in air, then the intensity, I, should vary inversely as the square of the distance between the source and the detector.’[2]

Air acts as an almost transparent medium to γ-rays, and the intensity (rate of energy arrival per unit area)

...read more.

Middle

[11]

Corrected count rate against 1/(d + d0)2 should produce a straight-line graph, passing through the origin, if the inverse square law is followed.

image06.jpg

Source: ’A Laboratory Manual of Physics’ –F. Tyler, Page 269

The 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=λN. The decay constant, λ, can be calculated using λ = ln2/t1/2 where the value for the half-life of Co-60 is 5.2714 years[13].

Therefore:

 λ = ln2/t1/2
    = 0.693/1.664 x 108
   = 4.175 x 10
-9

The gradient of the straight line graph will equal λN0e-λt so λ = gradient/ N0e-λt

 Safety Precautions:

To 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 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 thoroughly 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 radiate 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 items

Errors:

...read more.

Conclusion

Start the stopclock and measure the background radiation for an adequate length of time, e.g. 25 minutes, as background radiation is variablePlace the holder containing the γ-source at 5.0 cm from the window of the G-M tubeStart the stopclock and stop after 10,000 counts are registered. Record this value and repeat twiceMove the γ-source to 10.0 cm from the window of the G-M tube and repeat procedure 5, instead only counting 5000 countsMove the γ-source to 15.0 cm from the window of the G-M tube and repeat procedure 5, instead counting only 1000 countsRepeat procedure 7 for sets of 5.0 cm until a distance of 30.0 cm is reachedTabulate these results and find the average count rate for each distanceEvaluate 1/(d + do)2Using the recorded value for background radiation, evaluate the corrected count rate for each distancePlot the graph of corrected count rate against 1/(d + do)2




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[1] http://hyperphysics.phy-astr.gsu.edu/Hbase/forces/isq.html

[2]Essential Pre-University Physics’ – Whelan & Hodgson, page 953

[3] ‘Essential Principles of Physics’ – Whelan & Hodgson, page 472

[4] ‘Essential Principles of Physics’ – Whelan & Hodgson, page 472

[5] ‘Essential Principles of Physics’ – Whelan & Hodgson, page 472

[6] http://www.imagesco.com/articles/geiger/03.html

[7] http://en.wikipedia.org/wiki/Breakdown_voltage

[8]‘Essential Pre-University Physics’ – Whelan & Hodgson, page 406

[9] http://www.imagesco.com/articles/geiger/03.html

[10]http://en.wikipedia.org/wiki/Background_radiation

[11] ‘Advanced Level Practical Physics’ - M Nelkon & JM Ogborn, page 218

[12] ‘A Laboratory Manual of Physics’ – F. Tyler, page 269

[13]http://en.wikipedia.org/wiki/Cobalt

  • [14]
  •  ‘Advanced Level Practical Physics’ – M Nelkon & JM Ogborn, page 212

[15] http://en.wikipedia.org/wiki/Cobalt

...read more.

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