Write down the equation for the surface area of that

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Write down the equation for the surface area of that sphere. 2. On the surface of the sphere you’ve drawn, sketch an area representing a small particle detector. If the source emits radiation evenly in all directions, write an equation for the fraction of its radiation that would pass through the particle detector as a function of the area of the detector and the radius of the sphere. 3. Now draw another even larger sphere still centered on the radioactive source. Draw the same particle detector on the surface of the larger sphere. Now write an equation for the fraction of the source’s radiation that would pass through the particle detector as a function of the area of the detector and the radius of the new sphere. Is the rate of particles passing through the detector when it is on the surface of the larger sphere higher or lower than its rate when it is on the smaller sphere? 4. Write an equation for the relationship of a detector's counting rate and its distance from radioactive source. Sketch a graph of this relationship. What assumptions does this relationship require? 191
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DISTANCE FROM SOURCE – 1202Lab8Prob1 P REDICTION Use geometry to calculate how the particle count rate varies with distance from a small radioactive source. On what assumptions is your calculation based? E XPLORATION WARNING: The radioactive sources available for this problem provide low intensity radiation, and are safe if handled with respect for short amounts of time. Do not remove them from the laboratory, and do not attempt to open the plastic disks containing the sources. If a disk breaks open inform your TA immediately, do not touch it. Make sure you read the Equipment and Software appendices to understand the operation of the Geiger counter before trying to operate it. Place a radioactive source near the detector, turn on the counter. Try the controls, and make sure every group member understands how to operate it. Try each of your sources to make sure the equipment is functioning . With the detector working you now need to determine how to make your measurement uncertainty as small a practical. Start by using the detector to measure the number of counts from a radioactive source in some short time interval, say 10 or 15 seconds. Repeat this measurement several times, recording the number of counts occurring in each fixed time interval. Compute the average number of counts per second and the difference of each trial from that average. Calculate the average of these differences for all of your trials. That average difference represents your counting uncertainty for the measurement. Now increase your time interval by a factor of 4 and repeat the same number of trials and the same calculation. In which case is the measurement uncertainty a smaller fraction of the measurement? By approximately what factor did the average measurement change when you increased the counting time by a factor of 4? What does this tell you about the time period necessary when taking data? Keep
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