Nuclear Radiation and Radioactivity The 22 Na isotope is the most common source
ID: 1467783 • Letter: N
Question
Nuclear Radiation and Radioactivity The 22 Na isotope is the most common source material of positrons used in the research, with a half-life of 2.6 years. To avoid radiation exposure the 22Na-source is stored in a lead shielded container. Write a nuclear reaction for the 22Na decay Suppose in your laboratory there is such a source yielding a dose rate of 17 mrad/h at a distance of 1.0 m for an average-sized person. If workers are allowed a maximum dose of 5.0 rem within one year, how close to the source may they operate, assuming 35-h work per week? Assume that the intensity of radiation falls off as a square of the distance 1/r^2. (It actually falls off more rapidly because of the absorption in the air, but the value you obtain will be on a safe side).a Calculate how the dose rate of the source changes after one year passed. What is the new value in mrad/h? After one year passed what would be a new permissible distance at which the workers be able to operate the source without exceeding the maximum dose limit.Explanation / Answer
22Na emit gamma radiations
For gamma rays, 1 rad = 1 rem
For 1 m distance,
For 1 hr, 17 mrad is absorbed
For 1 week, 17 x 35 mrad is absorbed
For 1 year (52 weeks), dose = 17 x 10-3 x 52 x 35 = 30.94 rem.
But the dose must be only 5 rem
At 1 m from the source, dose = 30.94 rem
At x m, 30.94/x2 = 5
x = sqrt[30.94/5] = 2.49 m.
3.
N1 is the initial amount of the radioactive substance
After 1 year it became N2
kN1 = -[dN1/dt] = 17 mrad/hr ...(1)
kN2 = -[dN2/dt] ...(2)
k = 0.693/t1/2 = 0.693/2.6 = 0.2665 per year
N2 = N1 exp-[kt] = 0.766 N1
Substituting the above equation in (2)
k x 0.766 N1 = -[dN2/dt] ...(3)
(3) / (1) gives
[dN2/dt] = 17 mrad/hr x 0.766 = 13.022 mrad/hr.
4. Same way as 2 instead of 17, insert the value 13.022
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