Which Mattress Offers Better Protection Against Radioactive Pea: Lead or Cotton?

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SUMMARY

The discussion focuses on evaluating the protective capabilities of a 3cm thick lead mattress versus a 0.5m thick cotton mattress against radiation emitted by a highly radioactive pea doped with 65Zn. The radiation dose received is influenced by the inverse square law and the absorption coefficients of the materials. The lead mattress is expected to provide superior shielding due to its density and thickness compared to the cotton mattress, which has a significantly lower density of 0.10 g/cm3. Participants emphasized the importance of understanding the attenuation coefficients for accurate calculations of radiation exposure.

PREREQUISITES
  • Understanding of radiation physics, specifically gamma radiation and its interaction with matter.
  • Familiarity with the inverse square law as it pertains to radiation exposure.
  • Knowledge of absorption coefficients and their role in radiation shielding.
  • Basic grasp of Planck's Radiation Formula and its applications in thermal radiation calculations.
NEXT STEPS
  • Research the attenuation coefficients for lead and cotton to determine their effectiveness in radiation shielding.
  • Learn about the inverse square law in the context of radiation exposure and its practical applications.
  • Explore the relationship between density and absorption depth for various materials used in radiation protection.
  • Investigate the properties of gamma rays emitted by 65Zn and their implications for radiation safety.
USEFUL FOR

This discussion is beneficial for physicists, radiation safety professionals, and anyone involved in material science or health physics, particularly those interested in radiation shielding and protection strategies.

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Homework Statement



In order to be granted tenure, you are required to spend the night on a mattress below which has been placed a highly radioactive pea. You may choose either a solid lead mattress which is 3cm thick or a cotton mattress (considered to be made of carbon of density 0.10 g/cm^3) which is 0.5 m thick. Assuming the pea has been doped with 65Zn, calculate the relative amount of protection afforded you by each mattress- i.e. the ratio between the doses you get in each case. Assume the thickness of the mattress equals the distance from the pea to the nearest spot on your skin (in the small of your back assuming you sleep on your back). Also assume most of th gammas which Compton scatter won't reach you, so you can use the sum of absorption and scattering cross sections. Calculate you are most concerned about reducing the dose to the most exposed cubic centimeter of your body.

Homework Equations



I know 65Zn=.330188 Roetgens/hr 1m from 1curie
density of Zn=6.92 g/cm^3

I know the amount of radiation you receive is proportional to the amount of time spent near the source and for distance is proportional to the inverse square law. I also know shielding protects against radiation, but I'm not sure what sort of proportionality I should use.

I know the depth of penetration from radiation is 1/absorption coefficient. However I do not know how to get the absorption coefficient.

I've also worked out Planck's Radiation Formula for the pea with radius = 1cm.
P=alphaAT^4=(5.67*10^8)(4pi)(294)^4=5323 W

So I guess what I need help on is where to look next.
 
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You need to know the energy of the Gamma rays emitted. Absorption coefficients are tabulated here:http://physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html"

you want the attenuation coefficient, which includes scattering reactions. See the links at the bottom of that page. These have to be multiplied by the density of the material to get the absorption depth.

Planck's radiation formula has nothing to do with nuclear reactions
 
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