Radioactive Emission: Determining Half-Life

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SUMMARY

The discussion focuses on determining the half-life of a radioactive source emitting electrons, governed by the differential equation dN/dt = −1.8 × 10−5N(t). Starting with an emission rate of 12 electrons/sec at t = 0, the goal is to find the time when the emission rate falls to 4.0 electrons/sec. The half-life is defined as the time required for the emission rate to decrease from 12 electrons/sec to 6 electrons/sec, which directly correlates with the decay process described by the equation.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Knowledge of radioactive decay concepts and half-life calculations.
  • Familiarity with the mathematical relationship between decay rates and time.
  • Basic proficiency in solving exponential decay problems.
NEXT STEPS
  • Study the derivation of the half-life formula from the decay equation dN/dt = −λN.
  • Learn how to apply the exponential decay model in practical scenarios.
  • Explore numerical methods for solving differential equations in physics.
  • Investigate the implications of half-life in various fields, such as nuclear physics and radiometric dating.
USEFUL FOR

This discussion is beneficial for students in physics, particularly those studying nuclear physics, as well as educators and anyone interested in understanding radioactive decay and its applications.

henryc09
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Homework Statement


A radioactive source emits electrons. The number of electrons emitted per second
N(t) decreases with time according to the equation:

dN/dt = −1.8 × 10−5N(t) ,
where t is expressed in seconds. If N = 12 electrons/sec at t = 0, after what time t
has N fallen to the value 4.0 electrons/sec? [7]
What is the half-life of the radioactive source in seconds? [3]


Homework Equations





The Attempt at a Solution


I have the first part done, but am confused about the second part. How can you tell the half life of the material from the information given? N is just the amount of electrons given off per second, and the half life is the amount of time taken for the amount of substance to halve right? I don't see how they can be directly related. Any ideas?
 
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One way is to just work out how long it takes for the number of electrons given off per second to drop from 12 to 6. That represents the half-life time.
 
OK I was thinking that must be the only way. Thanks :)
 

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