Is There a Shortcut for Solving Half-Life Decay Equations?

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    Decay Half-life
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Discussion Overview

The discussion revolves around finding a shortcut for solving half-life decay equations, specifically in the context of a magnesium-27 sample that decays by 7% of its previous mass every minute. Participants explore various methods for determining the half-life and express interest in simplifying the process beyond traditional tabular methods.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Exploratory

Main Points Raised

  • One participant questions the lengthy process described in their textbook for determining half-life and seeks a more efficient method.
  • Another participant suggests that using a table to track the decay over time may be beneficial, given the nature of the decay process.
  • Some participants propose deriving a general expression for the remaining mass after a given time, encouraging others to identify patterns in the decay ratios.
  • A participant asks for a general formula for decay chains involving elements with different half-lives, indicating interest in more complex decay scenarios.
  • One participant mentions that the appropriate formula depends on the specific information desired and suggests using integrals to derive necessary results.
  • A later reply presents a mathematical expression related to the decay process, indicating a specific approach to finding the half-life.

Areas of Agreement / Disagreement

Participants express varying opinions on the best method to approach the problem, with no consensus on a singular shortcut or formula. Multiple competing views on how to simplify the process remain evident.

Contextual Notes

Some participants note the simplicity of the question, while others imply that the complexity of decay chains may require different considerations. There is no resolution on the best approach to take.

Who May Find This Useful

This discussion may be of interest to students seeking efficient methods for solving half-life decay problems, as well as those exploring the mathematical foundations of decay processes in physics.

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A 100 mg sample of magnesium-27 decays by 7% of its previous mass every minute. Determine its half-life and start the half-life decay equation.

The textbook that I got this from (Nelson Physics 11) tells me the answer, but uses a long and annoying process to find it: creating a table at different points in time and then graphing. I am just wondering if there is an equation or some sort of trick to this type of question? It would save me a lot of time and trouble, thank you in advance.
 
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It's a series.. it tells you that at each minute it loses 7% of what it had before... So it's better to use a table and see it...
 
Yes, it is very possible to derive a general expression for the amount left after a given time. If the sample loses 7% of its mass every minute, what is the ratio of mass left to original mass after 1 minute? What is the ratio after two minutes? Three minutes? Do you see a pattern? In that case, what should be the mass left after a time T?
 
To honour the "Compound" in the title of the post... Can someone point to the general formula for a decay chain, with elements having different half-lifes?
 
The right formula depends on what you want to know, but it is possible to get everything with the right integral for the considered problem.
 
The question seems too simple.
##\exp(-t/\tau)=0.93##, so ##\tau=-1/\ln(.93)## in minutes.
 
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