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

In summary, the californium-242 nucleus 242/98 Cf decays via alpha decay with a half life of 210s. If we originally have 10 000 californium-242 nuclei, how many will remain as californium after one half-life? Explain. If we originally have 10 000 californium-242 nuclei, how many will remain as californium after five half-life? Explain.
  • #1
3
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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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  • #2


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.
 
  • #3


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.
 
  • #4
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:
  • #5


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.
 
  • #6


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
 
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  • #7


i just figured out everything thanks!
 

1. What is Californium-242 and how does it decay?

Californium-242 is a radioactive isotope with 242 neutrons and 98 protons. It undergoes alpha decay, in which it emits an alpha particle (two protons and two neutrons) from its nucleus, transforming into a different element.

2. What is the half-life of Californium-242?

The half-life of Californium-242 is about 162.8 days. This means that after 162.8 days, half of the original amount of Californium-242 will have decayed into a different element.

3. What is the energy released during the alpha decay of Californium-242?

The energy released during the alpha decay of Californium-242 is about 6.1 MeV (mega-electron volts). This energy is released as the alpha particle is emitted from the nucleus.

4. What are the potential uses of Californium-242 in scientific research and industries?

Californium-242 is used in a variety of industries and scientific research, such as in nuclear reactors for neutron production, in medical treatments for cancer, and in measuring the thickness of materials using neutron radiography.

5. How is the decay of Californium-242 measured and detected?

The decay of Californium-242 can be measured and detected through various methods, such as through its radioactive emissions (alpha particles, gamma rays, and neutrons), by measuring the change in mass of the sample over time, and by using specialized detectors such as a Geiger counter or a scintillation counter.

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