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

[kchkwan]

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?

 

[Bob_for_short]

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.

 

[genneth]

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]

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 e^y = x, then ln(x) = y …

both e^x 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

 

[Bob_for_short]

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.

 

[kchkwan]

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

 

[kchkwan]

i just figured out everything thanks!