Calculation: radioactivity [atoms/ccm]

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SUMMARY

The calculation of radioactivity in contaminated water at Three Mile Island reveals that the concentration of Cs-137 is approximately 7.892E15 atoms/cm³ and Cs-134 is about 9.045E15 atoms/cm³. The activity of Cs-137 was calculated using the formula A = R*N, where R is derived from the half-life of 30.07 years, resulting in a decay constant of 6.4E-6 sec⁻¹. The conversion factors for time were crucial, utilizing 3600 seconds per hour, 24 hours per day, and 365.25 days per year to accurately compute the activity in Bq/cm³.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with the decay constant calculation
  • Knowledge of unit conversions in physics
  • Proficiency in using the activity formula A = R*N
NEXT STEPS
  • Study the principles of radioactive decay and half-life calculations
  • Learn about the significance of Bq (Becquerel) in measuring radioactivity
  • Explore advanced unit conversion techniques in scientific calculations
  • Investigate the implications of radioactivity in environmental science
USEFUL FOR

Students in physics or environmental science, researchers in radioactivity, and professionals involved in nuclear safety and contamination assessment will benefit from this discussion.

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Homework Statement



The problem:
4000,000 gal of water remained in a contaminated building at 3 mile island. The principle sources of radioactivity were:
137Cs at 156E-6 Ci/cubic cm and 134Cs at 26E-6 Ci/ccm. How many atoms/ccm were in the water?

Homework Equations


137E-6*3.7E10 Ci= 5.77E6 Bq/ccm
A ctivity= R*N
R= Ln2/T1/2

The Attempt at a Solution


R= Ln2/30.07yrs*3600s = 6.4E-6/sec
A = R*N
N = 5.77E6(decays/sec-ccm)/6.4E-6(1/sec) = 9.02E11 atoms/ccm

The given answers:
Cs-137: 7.892E15 atoms/cm3
Cs-134: 9.045E15 atoms/cm3
 
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R= Ln2/30.07yrs*3600s = 6.4E-6/sec

Be careful with conversions. There are 3600 s/hr, 24 hrs/day and 365.25 days/yr, or about 3.156 E7 s/yr.
 

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