How Many Atoms per Cubic Centimeter Are in Radioactive Water After Cleanup?

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SUMMARY

The discussion focuses on calculating the number of atoms per cubic centimeter in radioactive water after cleanup at Three Mile Island, specifically concerning the isotope Cesium-137 (Cs-137). The initial activity is given as 156E-6 Ci/cubic cm. To find the number of atoms, the calculation involves converting Curie to decays per second and using Avogadro's number, resulting in approximately 6.86E17 atoms per cubic centimeter. The complexity arises from needing to consider the decay rate and half-life of Cs-137 for accurate calculations.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with Curie (Ci) as a unit of radioactivity
  • Knowledge of Avogadro's number (6.022E23)
  • Basic proficiency in unit conversions and scientific notation
NEXT STEPS
  • Research the half-life of Cesium-137 and its implications for radioactive decay
  • Explore the concept of activity in radioactivity and its measurement units
  • Learn about the calculation of atoms from radioactivity using Avogadro's number
  • Investigate methods for measuring radioactivity in contaminated water
USEFUL FOR

Students in nuclear physics, environmental scientists, and professionals involved in radioactive waste management will benefit from this discussion.

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Homework Statement


"After cleanup at 3 mile island approximately 400,000 gal of radioactive water remained in the basement of the contaminated building. The principle sources of radioactivity were 137 Cs at 156E-6 Ci/cubic cm. How many atoms per cubic cm were in the water ?

Homework Equations


Not sure...

The Attempt at a Solution



6.022E23 * 156E-6/137 = 6.86E17
 
Last edited:
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It's a little more complicated than that.

A Curie (Ci) is 3.7E10 decays/second - so there are 156E-6 * 3.7E10 decays/sec/cc.

Then you need the activity or half-life of Cs137 to know what chance there is of a decay in a second for one atom, or alternatively how many atoms there needs to be to give the above overall decay rate.
 

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