Californium-242 nucleus 242/98 Cf decays via alpha decay

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Discussion Overview

The discussion revolves around the decay of the californium-242 nucleus (242/98 Cf) via alpha decay, specifically addressing questions related to its daughter nucleus, the remaining quantity after one half-life, and the remaining quantity after five half-lives. The context is primarily homework-related, focusing on the application of the decay law equation.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • The original poster (OP) seeks clarification on the decay law equation and its variables, specifically asking about the daughter nucleus and calculations related to half-lives.
  • Some participants propose that the decay law equation is N(t) = N e^(-λt), where λ is the decay constant, and they discuss the meaning of the variables involved.
  • One participant mentions that the half-life is not the same as the decay lifetime, indicating a potential misunderstanding in the OP's approach.
  • Another participant provides the value of e (approximately 2.718) and explains its relevance to natural logarithms, suggesting that the OP should use this in their calculations.
  • The OP expresses confusion about the logarithmic aspects of the equation and indicates a lack of familiarity with these concepts due to their current level of study.
  • In a later post, the OP attempts to apply the equation but arrives at a seemingly incorrect result, indicating ongoing uncertainty about the calculations.
  • Ultimately, the OP claims to have figured everything out, although the details of this resolution are not provided.

Areas of Agreement / Disagreement

Participants generally agree on the structure of the decay law equation and the importance of understanding the variables involved. However, there is no consensus on the OP's calculations or understanding of logarithmic functions, as the OP expresses confusion and uncertainty throughout the discussion.

Contextual Notes

The discussion reveals limitations in the OP's understanding of logarithmic functions and their application in the decay law, as well as potential confusion between half-life and decay lifetime. These aspects remain unresolved within the conversation.

Who May Find This Useful

This discussion may be useful for first-year students studying nuclear decay, particularly those seeking help with applying decay equations and understanding the concepts of half-life and decay constants.

kchkwan
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Hey I'm new to this forum, just want to say hi! I'm not sure if this is the rite place to put this but sry if i posted in the wrong section >.<

I'm actually working on an assignment in my natural science course and I'm stuck on this question cause I'm not sure how to use the variables in the equation.


The californium-242 nucleus 242/98 Cf decays via alpha decay with half life of 210s
A)what is its daughter nucleus?
B) if we originally have 10 000 californium-242 nuclei, how many will remain as californium after one half-life? Explain
C)if we originally have 10 000 californium-242 nuclei, how many will remain as californium after five half-life? Explain

Ok so how I view this... I need to use the Decay Law equation to find the daughter nucleus rite? since its going through alpha decay.

So equation would be N(t) = N e^(-λt)
N(210) = N e^(-λ210)

is N = 242?
So... wuts e? and λ?
 
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kchkwan said:
Hey I'm new to this forum, just want to say hi! I'm not sure if this is the rite place to put this but sry if i posted in the wrong section >.<

I'm actually working on an assignment in my natural science course and I'm stuck on this question cause I'm not sure how to use the variables in the equation.


The californium-242 nucleus 242/98 Cf decays via alpha decay with half life of 210s
A)what is its daughter nucleus?
B) if we originally have 10 000 californium-242 nuclei, how many will remain as californium after one half-life? Explain
C)if we originally have 10 000 californium-242 nuclei, how many will remain as californium after five half-life? Explain

Ok so how I view this... I need to use the Decay Law equation to find the daughter nucleus rite? since its going through alpha decay.

So equation would be N(t) = N e^(-λt)
N(210) = N e^(-λ210)

is N = 242?
So... wuts e? and λ?

The decay law N(t) is the number of nuclei survived the decay. It decreased with time. N(0)-N(t) is the number of decayed nuclei. It increases with time. Lambda is 1/(210s), N=10 000, e=2.72 (do you know natural logarithms?).

Bob.
 


Bob_for_short said:
Lambda is 1/(210s)

Careful there. Half life != decay lifetime.

In any case, the OP seems to need homework help, so it would be good for a moderator to move this there.
 
Welcome to PF!

Hey kchkwan! Welcome to PF! :smile:
kchkwan said:
The californium-242 nucleus 242/98 Cf decays via alpha decay with half life of 210s
…
So equation would be N(t) = N e^(-λt)
N(210) = N e^(-λ210)

is N = 242?
So... wuts e? and λ?

e = 2.718281828459 …

it's the base of the natural logarithms (ln), so if ey = x, then ln(x) = y …

both ex and ln(x) should be on your calculator.

And the half-life is ln(2)/λ = 0.69314/λ …

see the https://www.physicsforums.com/library.php?do=view_item&itemid=193" entry for details :wink:
 
Last edited by a moderator:


genneth said:
Careful there. Half life != decay lifetime.

In any case, the OP seems to need homework help, so it would be good for a moderator to move this there.

You are right, I missed the logarithm. The tim's answer is correct.

Bob.
 


Hiii thanks for the help everyone!

but I'm only a first year student and i haven't really learned anything else other than that equation, so any of the log stuff i haven't learned yet. I'm just going to try readin over this and see if i can get an answer lol

thanks!

EDIT* ok so my Equation is now this rite?

N(210) = 242(2.72)^-(0.69)(210)
= 25490.06?

and that's 1 half life? O_O lol... I am so lost on this question for some reason XD
 
Last edited:


i just figured out everything thanks!
 

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