Exponential Attenuation and Beta Particle Range

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SUMMARY

The discussion focuses on calculating the range of beta particles in air using the law of exponential attenuation, specifically the equation I=I0e^(-ux). The user is tasked with determining the range based on a beta emitter with a mass difference of 0.0034 amu between the emitter and its daughter. Key insights include the importance of not setting intensity (I) to zero, as this occurs only at infinity, and the need to identify a characteristic length scale where intensity decreases by a factor of e.

PREREQUISITES
  • Understanding of exponential attenuation laws in physics
  • Familiarity with mass attenuation coefficients
  • Knowledge of beta decay and particle physics
  • Basic proficiency in logarithmic functions and their applications
NEXT STEPS
  • Research the calculation of mass attenuation coefficients for beta particles
  • Study the relationship between energy, intensity, and flux in particle physics
  • Explore characteristic length scales in exponential decay processes
  • Learn about the implications of mass defect in nuclear reactions
USEFUL FOR

Students and professionals in nuclear physics, particularly those studying beta decay, as well as educators preparing lessons on exponential attenuation and its applications in radiation physics.

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Exponential Attenuation and Beta Particle Range (solved)

Homework Statement


I am given a beta emitter and its atomic mass, as well as the atomic mass of its daughter, which have a difference of 0.0034 amu. I am to determine the range of the particles in air.

Homework Equations


I am given the law of exponential attenuation:
I=I0e^(-ux)
And substituted for mass attenuation coefficient:
I=I0e^(-um*px)
um and p(rho) are readily available, and can be considered given

The Attempt at a Solution


So I am looking for x, but I do not know I0 (is there some relation between mass or energy and intensity?), and if I'm looking for the range, I assume I to be 0 (if intensity is energy flux x velocity, at the end of the range it must approach 0) which opens up all sorts of nasty when we try to find ln0 (which, essentially approaches infinity).
 
Last edited:
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1. What is the relevance of the mass defect?

2. You can not set I=0, because that will only happen at x=infty, which is useless.

3. You want to find a characteristic length scale, typically the distance over which the intensity drops by a factor of e.
 

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