Sec. 10.15] GEIGER-MULLER COUNTERS 321 



deviation of the background count a b as well as of the sample plus background 

 a s and is given by 



o- = V<rl + a 2 s = \/N b + N a counts 



N b and N s are the number of registered counts for background and the sample 

 plus background taken over equal intervals of time. 



10.15. Probable Error. The probable error r is calculated from the 

 standard deviation <r or directly from the total number of counts of the sample 

 plus background, N s , and the total background count A T 6 counted for the 

 same length of time. The probable error in number of counts is 



r = 0.6745<r = 0.6745 y/N, + N b counts 



In terms of per cent, 



67.45 /T^-T-rr 



r = m vt v A » + N >> % 



u\ s — Mb) 



It is seen that, like the standard deviation, the probable error may be 

 calculated from the total number of counts N or from the M sets of measure- 

 ments. 



The probable error defines limits, ±r, about the mean value, N counts 

 in time t, or n cpm, within which any single measurement of the activity 

 should occur with a probability of 0.5 and with an equal probability for all 

 values outside these limits. 



When the approximate values of the sample and background counting 

 rates are known, it is frequently more convenient to count samples by time 

 intervals rather than by total events. When the sample plus background 

 and the background are counted separately to give the same relative probable 

 error, the minimum time required to reduce the total statistical error of the 

 sample measurement to a prescribed percentage r is given by 



9,100w 



/ = -jrrz rr, mm 



r-{n — n b )- 



and for the background, the minimum counting time should be 



(n — n b )H 



h = — mm 



ntii, 



where n = average counting rate of sample plus background 



fi b = average counting rate of background 

 The true value of h — n b is then calculated with the prescribed accuracy 

 from the total counts N in the time t and background counts N b in the 

 time t b . 



When possible, lead shielding should be used to reduce the magnitude 

 of the background counting rate and hence the required counting time. 



