Geiger Counter Experiments In this laboratory session we will do different experiments with the Geiger Counter determining the proper operating voltage estimating the efficiency and measuring the half life of Ba137m 1 Operating Voltage of the Geiger Counter First we will measure the Geiger counter s response as a function of applied voltage a Place a source under the Geiger counter tube b Set the timer to count for ten minutes or longer c Set the voltage to zero first then slowly turn up the voltage until the counter starts to record counts This is the starting voltage d Take 1 minute readings increasing the voltage by about 10 or 20 volts each time Make a table of your data Note to prevent damaging the tube do not increase the voltage more than 150 volts beyond the starting voltage and certainly not more than 1000 volts e Graph your results using Excel or on linear graph paper Label on your graph the starting voltage and the plateau region Also label the proper operating voltage on the graph From your graph do you think your Geiger counter tube is operating properly Why or why not 2 Efficiency of the Geiger Counter In this part you will estimate the efficiency of the Geiger Mueller tube for a particular source The efficiency of the Geiger counter will depend on the sample so be sure to record the sample used From the activity written on the source use the half life formula to determine the activity in decays sec of your source today Place your source as close to the tube as you can and count for 2 minutes Estimate the distance the source is away from the tube Determine the efficiency of the GeigerMueller tube for this positioning of the source We will define the efficiency as 1 particles detected particles emitted 1 Note If you use Cs137 as your source the yields are 100 for beta s 85 for gamma s and 8 for X rays That is for every 100 decays there are 100 beta s 85 gamma s and 8 X rays Since the Geiger counter can not differentiate between the different types of radiation we will just take the number of particles emitted to be equal to the number of decays 3 Statistical Analysis of the Decay Here we will do two exercises in examining the statistical nature of nuclear decay 1 Place a source under the Geiger Mueller tube Collect data for two minutes Record the number of counts Repeat the collection 30 times if time permits Your data will consist of 30 integers each one being the counts for two minutes Are all the integers equal i e do you get the same number of counts each time Find the average number of counts and the standard deviation If Ni represents the number of counts in measurement i then Nave P30 i 1 30 sP Ni 2 30 i 1 Ni Nave 2 29 3 Once you have found Nave and write your results on the board We will have a classroom discussion of our measurements 2 Next to the link for this experiment there is a file called time interval data There are 66000 numbers in the file The numbers are the times between successive Geiger Counter pulses in units of sec 10 6 sec Make a histogram of these times Initially try 100 sec as a bin size From the histogram estimate the dead time of the detector For the times after the dead time see if an exponential function fits the data What physics does this data support 4 Measurement of the half life of Ba137m 2 The half life of Ba137m is on the order of minutes In this experiment we will record the counts for the Ba137m source for a 10 second counting time We take these readings every 30 seconds Before you start the experiments make a data table similiar to the form below time sec Counts in 10 seconds 0 30 60 90 1 After the instructor places the sample under your Geiger Counter tube start recording data 2 After correcting for dead time and background make a graph of the number of counts sec as a function of time Fit the graph with an exponential function Determine the decay constant and half life from the slope of the graph Report for Experiment 1 1 Make a table and graph of Counts vs voltage for your Geiger counter tube Label on your graph the starting voltage operating voltage and the plateau region 2 Show your data and calculations for determining the efficiency of your Geiger counter 3 Show your data and calculations for the 30 2 minute recordings The calculations will be for the average number of counts Nave and the standard deviation Show the histogram plot of the time interval data Determine the dead time and the parameters of the exponential fit What physics do this data support 4 For the Ba137m decay use Excel to make a graph of counts sec vs time Include the corrections for background and dead time a Is the decay exponential i e does it obey the half life formula b If it does follow an exponential decay what is the half life of the decay 3 Decay rate of radioactive nuclei The exponential decrease of the decay rate as a function of time can be understood from one principle of nature Each radioactive nucleus has a certain probability to decay per unit time This probability does not depend on how long the nucleus has been in its excited state i e radioactive The probability to decay per unit time is denoted by the symbol and is called the decay constant of the decay has units of 1 time The probability that a particular nucleus will decay in the time interval is in the limit as 0 Our radioactive sample has a large number of radioactive nuclei N0 The probability that one nucleus will decay in the time interval is N0 in the limit as 0 If the efficiency of our detector is then the probability that our Geiger Counter tube will detect a particle in the time interval is N0 in the limit as 0 For convenience we define A N0 If the decay process is probabilistic then there exists a probability per unit time A such that the probability that our Geiger Counter tube will detect a particle in the time interval is A in the limit as 0 Suppose we have an isotope with a long half life Since the half life is long N0 hardly changes during our measurement We can ask the following question What is the probability Pnot that we will not record a count within a time t since the last count was recorded This can be answered as follows Divide the time t into N equal segments each of duration That is t N Then Pnot is given by Pnot 1 A N 4 Now we need to take the limit as 0 or as N Pnot lim 1 N At N N 5 This limit is the exponential to the base e Pnot e …