Half Life of radioactive element

Click For Summary

Discussion Overview

The discussion centers around the concept of half-life in radioactive decay, exploring the implications of half-life calculations and the nature of complete decay. Participants examine the mathematical treatment of half-life and its relationship to the concept of infinity in decay processes.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants assert that complete decay of a radioactive element takes an infinite amount of time, while half-life is defined mathematically as T-1/2 = ln 2 / lambda.
  • One participant questions the logic of doubling the half-life to reach a "full life" of the radioactive element, suggesting this leads to a contradiction with the concept of infinity.
  • Another participant clarifies that after each half-life, the remaining quantity is halved, leading to a diminishing amount but never reaching zero in a finite time.
  • Some argue that discussing a "full life" of a radioactive substance is misleading, as the assumptions of the half-life model become less valid with fewer radioactive atoms.
  • There is a contention regarding the interpretation of half-life decay as a statistical process, with some suggesting that the mathematical formalism may not apply at very small quantities of material.
  • One participant emphasizes that while mathematically one can approach zero, in practice, the decay process will eventually lead to a finite number of remaining atoms.

Areas of Agreement / Disagreement

Participants express differing views on the implications of half-life and the nature of decay, with no consensus reached on the interpretation of "full life" or the relationship between half-life and complete decay.

Contextual Notes

Limitations in the discussion include assumptions about the applicability of mathematical models to small quantities of radioactive material and the interpretation of decay processes as statistical versus deterministic.

abrowaqas
Messages
113
Reaction score
0
It takes an infinite time for complete decay of a radioactive element. but on the same time we calculate the half life of radioactive material i-e T-1/2 = ln 2 / lamda. is that means that if we double the half life time we could reach the total life time of radioactive decay so on contrary we have reached the infinity. which is impossible. how can this be cleared.
 
Physics news on Phys.org
Your statement is a little confusing. After one half-life, half the original material remains. After another half-life, one-quarter (half of half) remains. After another half-life, one-eighth remains, etc.
 
i said that if we double the half life that is we multiple the half life by two so we will get the full life of radioactive element... but how is this possible coz full life of radioactive element is at infinity... so what's the confusion here.
 
abrowaqas said:
i said that if we double the half life that is we multiple the half life by two so we will get the full life of radioactive element... but how is this possible coz full life of radioactive element is at infinity... so what's the confusion here.

Wrong,if you double the half life what you get is just that,double the half life or two half lives.It is misleading to talk about "full life" of a radioactive substance because one of the assumptions made in the mathematical treatment of half life becomes less valid as the number of radioactive atoms gets smaller.
 
I doesn't take infinity for the last bit of a quantity of a radioactive substance to decay. The process is a statistical one applicable to large numbers of particles and won't hold when you are right down there at small numbers. I think you are taking the mathematical formalism of radioactive decay a little too literally.
 
no youre wrong, half-life decay is like a log function, so doubling the time won't mean it would decay
 
abrowaqas said:
It takes an infinite time for complete decay of a radioactive element. but on the same time we calculate the half life of radioactive material i-e T-1/2 = ln 2 / lamda. is that means that if we double the half life time we could reach the total life time of radioactive decay so on contrary we have reached the infinity. which is impossible. how can this be cleared.

I believe that you are confusing radioactive decay with the mathematical function known as an infinite series. It is true that if you continue to divide any number by 2, you will never reach zero, although you will get infinitely close to it. But when you are dealing with a discrete number of items, such as atoms in a chunk of radioactive material, eventually you will get down to a very small number, say 8, then 4, then 2, then 1, then zero! Therefore, it is NOT an infinite series.
 

Similar threads

Undergrad Half life and radioactivity clarification
  • · Replies 20 ·
Replies
20
Views
3K
High School Shorter half-life and therefore very radioactive -- why?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Decay constant of Different Elements and Isotopes?
  • · Replies 3 ·
Replies
3
Views
2K
High School Can alpha radiation make other materials radioactive?
  • · Replies 9 ·
Replies
9
Views
5K
Undergrad How Often Are the Charge and Mass of High-Energy Cosmic Rays Identified?
  • · Replies 4 ·
Replies
4
Views
4K
High School Why do radioactive materials decay in half-lifes?
  • · Replies 6 ·
Replies
6
Views
2K
High School Is Radioactive Decay Truly Random?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Radioactivity in quantum physics
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Is there a tie between half life and energy of decay?
  • · Replies 3 ·
Replies
3
Views
2K
High School Calculating safe levels of radioactivity
  • · Replies 35 ·
2
Replies
35
Views
5K