(a) Verify that the chance on one throw of gettinga 7 is p = 1/6. (c) Find the probability of decay of a given atom of cesium in the 1-minute interval.10.9. (b) Find the standard deviation in the countingrate. (a) Assuming one count for each 50 disintegrations, find the expected counting rateand the number of counts for the interval. Counts are taken for a minute from a microcurie source of cesium-137, half-life 30.2years. What is the value of p in throwing a single die? Find xfor 1 or 2 throws of a die and calculate P(x) for each case.10.8. 10.6 is well approximated by thePoisson formula x( ) ( )P(x) ≅x / x! exp − x ,where x = pn is the mean value of x. For a situation in which the chance of success p is much smaller than 1, the probabilityof x successes in n trials in the binomial formula of Ex. (c) repeat the above calculations using program STAT (see Computer Exercise 10.A).10.7. (b) apply to throwing a single die 1 or 2 times, finding the number of sixes. (a) apply to flipping a coin l, 2 and 3 times, finding the number of times the result isheads, including zero. The probability of x successful events in n trials, each of which has a chance p, is givenby the binomial distribution formula,Ĭomputer Exercises 125( )P(x) = n! p x (1− p)n−x / (n − x)!x!. How many electrodes would be required in a photomultiplier tube to achieve amultiplication of one million if one electron releases four electrons?10.6. If r1 = 1 mm and r2 = 1 cm, what fraction of thepotential difference exists within a millimeter of the wire?10.5. In a gas counter, the potential difference at any point r between a central wire of radiusr1 and a concentric wall of radius r2 is given by ( )V = V0 ln r / r1, ( )ln r2 / r1where V0 is the voltage across the tube. If we observe in a period of 1 day a total count of 50,000 in a counter that detectsall radiation emitted, how many atoms were initially present?10.4. We collect a sample of gas suspected of containing a small amount of radioiodine, half-life 8 days. Discuss theeffect of collisions on the collection time.10.3. If the gas pressure isvery low, estimate the ratio of the times elapsed until the charges are collected. Ion halfwaybetween two parallel plates with potential difference between them.
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