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

## Main Question or Discussion Point

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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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.

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.

tiny-tim
Homework Helper
Welcome to PF!

Hey kchkwan! Welcome to PF! 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 Last edited by a moderator:

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 gonna 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 thats 1 half life? O_O lol... im so lost on this question for some reason XD

Last edited:

i just figured out everything thanks!