Question description

 

Name ____________________

1. In class we performed a nuclear counting experiment where we studied the decay of Co60. This sample was chosen because it has a long “half life” (the time it takes for half of the nuclei to decay). So during the 30 minutes of data collection, we could expect that the number of nuclei did not change significantly. Thus, we expected the number of decays to be randomly distributed about a center value according to the Gaussian distribution.
2. Taylor 5.12: The width of a Gaussian Distribution is usually characterized by the parameter s. An alternative parameter with a simple geometrical interpretation is the full width at half maximum, or FWHM. This is the distance between the two points x where fX,s (x) is half its maximum value, as in figure F.18 below. Prove that
3. Taylor 5.20: An extensive survey reveals that the heights of men in a certain country are normally distributed, with mean h=69” and standard deviation s = 2”. In a random sample of 1000 men, how many would expect to have height
4. Taylor 5.35: A student measures g, the acceleration of gravity, repeatedly and carefully, and gets a final answer of 9.5 m/s2with a standard deviation of 0.1 m/s2. If his measurements were normally distributed, with the center at the accepted value 9.8 m/s2 and with a width 0.1 m/s2, what would be the probability of getting an answer that differs from 9.8 m/s2 by as much as (or more than his? Assuming that he made no actual mistakes, do you think it is probable that his experiment suffered from some undetected systematic errors?
5. After measuring the speed of sound u several times, a student concludes that the standard deviation sd of the measurements is sd = 10 m/s. Assuming that the errors are all random, the student can get any desired precision by making enough measurements and averaging. How many measurements are needed to give a final uncertainty of +/- 3 m/s? How many for an uncertainty of .02only 0.5 m/s?

If we were to look at a sample with a short half-life or look at Co60 over a long time frame, then we would expect the number of nuclei to decay according to the theoretical equation derived in class:

This can be re-written by considering the probability function f(t) = N(t)/No so that.

where A is the normalization constant and .

• a)Calculation: Integrate to show that, for f(t) to be normalized, A = 1/t.
• b)Program: In class we wrote a LabView program to display the Gaussian function using a formula node. Modify this program to graph the function above for t between 0 and 10 seconds and Copy your front and back panel screens and paste them into your document for submission.
• c)Calculation: Calculate the mean time <t>, where . From this, give a physical meaning to the symbol .
• d)Program: Determine the percentage of nuclei which would have decayed after 6 seconds. Again, copy your program front and back panel and paste it onto your HW for submission.

• a)Between 67” and 71”
• b)More than 71”
• c)More than 75”
• d)Between 61” and 66 ”
• e)More than 66.5”

Note: You can use your program for this problem.