Hi, can someone please help me with my pre-lab question? I know it seems long an

Question

Hi, can someone please help me with my pre-lab question?

I know it seems long and complecated.. but I would be really appreciated if you could do this for me!

Thank you so much !

1. Counting statistics:

If you stand by a busy freeway couting cars for 10 minutes, and you cound 400 cars, what is:

(a) the number of cars per minute, and

(b) the percentge uncertainty in this result (Remember that the uncertainty depends on the total number of itmes, not the rate?)

Suppose you wanted to achieve a 1% uncertainty:

(c) How many minutes must you count cars?

2. The sources you will use in this Experiment are so weak they will give you a negligible dose, as explained above. However, there are other circumstancs in dealing with radiotactive sources, for example in nuclear medicine, where one must pay close attention to safety practices. Here you will carry out a couple of calculatios, Using Table 6-1, to compute the effects of the "natural shielding" of the 1/D^2 effect, and absorption by lead.

< Table 6-1 >

Mass Absoption Coefficients ( μ' = μ / p : cm^2 / g)

Photon Energy Water Aluminum Iron Lead

(MeV)

0.1 0.167 0.160 0.342 5.29

0.15 0.0149 0.133 0.182 1.84

0.2 0.136 0.120 0.138 0.895

0.3 0.118 0.103 0.106 0.335

0.4 0.106 0.0922 0.0918 0.208

0.5 0.0967 0.0840 0.0828 0.145

0.6 0.0894 0.0777 0.0761 0.144

0.8 0.0786 0.0682 0.0668 0.0837

1.0 0.0706 0.0614 0.0595 0.0683

1.5 0.0576 0.0500 0.0484 0.0514

2.0 0.0493 0.0431 0.0422 0.0451

Suppose that you had a source of 0.4 MeV gamma rays that exceeded a safe radiation level by a factor of 10 when it was held 10 cm from your body.

(a) What thickness of lead sheet should you use to enclose the source, to reduce your doe by a factor of 10?

(b) Alternatively, at what idstance should you keep the source from your body, if ther is there is only air between you and the source?

3. If one lead sheet reduced radiation by 1/2, by what factor whould the radiation be reduced if it passes through two of these lead sheets?

Explanation / Answer

1 a) 400/10 = 40 cars/minute


b) error in number = sqrt(40)

percent uncertainity = sqrt(40)/40 = 1/sqrt(40)=15.8%

c)
1/sqrt(n) = 0.01

n = 100^2

time = 100^2/40= 250 minutes

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