OBJECTIVE
To show that the intensity of radiation on a surface is inversely proportional to the square of the distance of the surface from the radiation source
MATERIALS AND APPARATUS
SUMMARY OF THEORY
Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena.
As one of the fields which obey the general inverse square law, a point radiation source can be characterized by the relationship below whether you are talking about Roentgens, rads or rems. All measures of exposure will drop off by inverse square law.
The source is described by a general "source strength" S because there are many ways to characterize a radiation source - by grams of a radioactive isotope, source strength in Curies, etc. For any such description of the source, if you have determined the amount of radiation per unit area reaching 1 meter, then it will be one fourth as much at 2 meters.
PROCEDURE
Initial Position: Distance from heat source (X) = 800mm.
1. Set power control to wide position and allow approximately 15 minutes for the heater to reach a stable temperature prior to starting the experiment.
2. Record the radiometer reading ( R ) and the distance from the heat source (X) for a number of positions of the radiometer along the horizontal track.
3. Allow approximately two minutes for the radiometer to stabilize after being moved to each new position.
4. Generate a log-log plot of radiometer reading against distance.
*Note that radiometer sensor surface is 65mm from center line of detector carriage and therefore center line position will be 865 mm.
DATA AND RESULTS
Using Microsoft Excel Application, the slope of the line of the graph above was solved using linear regression. The output for the regression for each trial is shown below.
SUMMARY OUTPUT
Coefficients
Intercept 6.162876527
Log Distance -1.673775219
Slope for Trial 1 = -1.67378
Slope for Trial 2 = -1.65939
Average Slope = -1.66658
CONCLUSION
Any object at elevated temperature gives off light known as thermal radiation. The hotter an object gets the more light it emits. As the temperature of the object increase, it emits most of its light at higher and higher energies. As one moves further from the source, the emitted particles are dispersed and are therefore less likely to strike the radiation measurement device. Since the area over which the emissions are dispersed is that of an expanding sphere about the source, the radiation intensity follows the inverse square law as one move away from the source
The experiment’s objective is to show that the intensity of radiation on a surface is inversely proportional to the square of the distance of the surface from the radiation source. As seen in the Figure 2, the two trials obtained similar results. As a matter of fact, these results were close enough to each data point making it unnecessary to take another trial since the first two trials are consistent with each other. The plot of the Log Distance vs. Log Radiometer Reading displays a line decreasing from left to right. This kind of configuration will give us a negative slope of the line. To prove the existence of the inverse square law of heat, the line must display a slope close to or equal to -2.0.
For each trial, a slope was calculated using linear regression of the MS Excel Application. Trial 1 gave a slope of -1.67378 while trial 2 gave a slope of -1.65939. Both trials gave an average slope of -1.66658.
To show that the intensity of radiation on a surface is inversely proportional to the square of the distance of the surface from the radiation source
MATERIALS AND APPARATUS
- Radiometer
- Heat source
Figure 1. Thermal Radiation Unit
Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena.
As one of the fields which obey the general inverse square law, a point radiation source can be characterized by the relationship below whether you are talking about Roentgens, rads or rems. All measures of exposure will drop off by inverse square law.
The source is described by a general "source strength" S because there are many ways to characterize a radiation source - by grams of a radioactive isotope, source strength in Curies, etc. For any such description of the source, if you have determined the amount of radiation per unit area reaching 1 meter, then it will be one fourth as much at 2 meters.
PROCEDURE
Initial Position: Distance from heat source (X) = 800mm.
1. Set power control to wide position and allow approximately 15 minutes for the heater to reach a stable temperature prior to starting the experiment.
2. Record the radiometer reading ( R ) and the distance from the heat source (X) for a number of positions of the radiometer along the horizontal track.
3. Allow approximately two minutes for the radiometer to stabilize after being moved to each new position.
4. Generate a log-log plot of radiometer reading against distance.
*Note that radiometer sensor surface is 65mm from center line of detector carriage and therefore center line position will be 865 mm.
DATA AND RESULTS
Figure 2. Plot of Log Distance vs. Log Radiometer Reading
Using Microsoft Excel Application, the slope of the line of the graph above was solved using linear regression. The output for the regression for each trial is shown below.
SUMMARY OUTPUT
Coefficients
Intercept 6.162876527
Log Distance -1.673775219
Slope for Trial 1 = -1.67378
Slope for Trial 2 = -1.65939
Average Slope = -1.66658
CONCLUSION
Any object at elevated temperature gives off light known as thermal radiation. The hotter an object gets the more light it emits. As the temperature of the object increase, it emits most of its light at higher and higher energies. As one moves further from the source, the emitted particles are dispersed and are therefore less likely to strike the radiation measurement device. Since the area over which the emissions are dispersed is that of an expanding sphere about the source, the radiation intensity follows the inverse square law as one move away from the source
The experiment’s objective is to show that the intensity of radiation on a surface is inversely proportional to the square of the distance of the surface from the radiation source. As seen in the Figure 2, the two trials obtained similar results. As a matter of fact, these results were close enough to each data point making it unnecessary to take another trial since the first two trials are consistent with each other. The plot of the Log Distance vs. Log Radiometer Reading displays a line decreasing from left to right. This kind of configuration will give us a negative slope of the line. To prove the existence of the inverse square law of heat, the line must display a slope close to or equal to -2.0.
For each trial, a slope was calculated using linear regression of the MS Excel Application. Trial 1 gave a slope of -1.67378 while trial 2 gave a slope of -1.65939. Both trials gave an average slope of -1.66658.