How can I calculate the rate of energy absorption from nuclear decay?

[Sorin2225]

Homework Statement

Started with a 0.1g of cesium-137, decayed into ba-137 after twelve hours by beta decay, this starts to decay with gamma rays. 12 hours after this someone pockets the sample and absorbs 50% of the beta particles and 10% of the gamma rays. How would I find the rate at which they are absorbing energy.

Relevant Equations

beta energy=0.512MeV
Gamma energy=0.6617MeV
Rate of Beta and gamma radiation=3.2*10^11

Problem Statement: Started with a 0.1g of cesium-137, decayed into ba-137 after twelve hours by beta decay, this starts to decay with gamma rays. 12 hours after this someone pockets the sample and absorbs 50% of the beta particles and 10% of the gamma rays. How would I find the rate at which they are absorbing energy.
Relevant Equations: beta energy=0.512MeV
Gamma energy=0.6617MeV
Rate of Beta and gamma radiation=3.2*10^11

Assuming it is 10% and 50% of the particles been released at 12 hours. So 10% of gamma = 3.2*10^10
50% of gamma = 1.6*10^11. This is how many particles are been emitted. Energy is per photon so 3.2*10^10 * 0.6617*10^6, 1.6*10^11* 0.512*10^6.. Energy of Gamma=2.11744*10^16. Energy of Beta= 8.192*10^16. Thus total energy would be these two added = 1.031*10^17. Over twelve hours so 8.59*10^15. I have no idea if this is even on the right track. The only other way I can think of doing it would be finding out the mass difference after the decay and using E=mc^2 but I assume I don't use that because I was given the energies.

 

[BvU]

I have honestly no idea how to even start

Hi,

Have you seen the guidelines ? We are not allowed to assist unless you post an effort ! Your relevant equations are not relevant equations, but parameters/variable values that are part of the problem statement.

What have you learned so far about decays that might be applicable ?

 

[Sorin2225]

Sorry about that, I have now added my initial attempt and we just get a textbook, but it doesn't seem to have anything about the energies of Decay. Just direction to a text that talks about it would be appreciated. I

 

[BvU]

Assuming it is 10% and 50% of the particles been released

I think the problem statement says that 10% and 50% of the particles that have been released are absorbed, and you are supposed to calculate the rates at which they are being emitted.

Google is your friend -- even for introductory material

 

[BvU]

Rate of Beta and gamma radiation=3.2*10^11

Is that a given ? Or did you calculate it ? How ?

 

[Sorin2225]

It's a given as the rate of emitting radiation after 12 hours.

 

[BvU]

anything about the energies of Decay

But you have them:

beta energy=0.512MeV
Gamma energy=0.6617MeV

 

[BvU]

Could you post the full problem description ? I don't understand the scenario: Cs doesn't stop decaying if you put it in your pocket ?!

In #1 you it seems are asked for a rate of energy consumption, not a total energy. Units ?

 

[Sorin2225]

A 0.1 g sample of pure Cesium-137 is produced.
Cesium-137 decays via β− emission into a metastable nuclear isomer of Barium-137 which in turn decays via the emission of a gamma-ray into stable Barium-137.
Cs-137 has a half-life of 30.17 years and the β− particle produced has an energy of 0.512 MeV.
Ba-137m has a half-life of 2.55 minutes and produces γ photons with an energy of 0.6617 MeV.
After 12 hours rate of sample emitting radiations= 3.203427×10^11

12 hours after being produced the sample is accidentally pocketed by a lab assistant. The lab assistant absorbs 50% of all β− particles and 10% of all γ-rays.
At what rate is the lab assistant absorbing energy from the sample?

As in dE/dt(absorbed) = ?

It's still decaying, but the person is only absorbing some of the energy from it.

 

[gleem]

Why was it said that the Cs sample was pocketed 12 hours after it was produced. Why is this important.

 

[Sorin2225]

Because the lab assistant put it in their pocket and so now they are absorbing radiation energy from the sample

 

[gleem]

No that is not the reason. What has happened in the sample that is important to the solution of this problem?

 

[Sorin2225]

It has decayed from Cs to Ba and continues to decay by emitting gamma and beta particles?

 

[gleem]

For what course is this problem from so I might determine how much you should know?

 

[Sorin2225]

University first year. New Zealand

 

[gleem]

What specific course e.g. Fundamental Nuclear Physics?

 

[Sorin2225]

fundamentals of physics

 

[gleem]

This is curious that they would specifically told you that the source was picked up 12 hrs after production. What is your knowledge of nuclear decay?

 

[Sorin2225]

For energy of nuclear decay, pretty much just that the change in mass would be related to the energy via e=mc^2.

 

[gleem]

What about half lifes?

 

[Sorin2225]

During every half life, half of the amount of sample will decay

 

[gleem]

How is half life related to the rate of radiation released?

 

[Sorin2225]

The rate of radiation rleased is just constant isn't it?

 

[gleem]

Yes, I just reread your post 9 stating the problem. You do not need to know about half lives. They give you the rate do radiation production i.e., 3.203427×10^11 disintegrations/sec. From the info in the problem each decay releases one beta(0.512 MeV) and 1 gamma(.662 MeV). Each is absorbed differently 50% of the Beta and 10% of the gamma. This is not so much of a physics problem as an algebra problem.