# Power generated by radioactive decay

1. Dec 3, 2014

### leehufford

1. The problem statement, all variables and given/known data
A radioactive source is to be used to produce electrical power from the alpha decay of 238 Pu (half life of 88 years).
a) What is the Q value for the decay?
b) Assuming 100% conversion efficiency, how much power could be obtained from the decay of 1.0 g of 238 Pu?

2. Relevant equations
λ = ln(2)/(88 years)
Number of nuclei = (mass)x(Molar Mass)x(Avogadro's number)

3. The attempt at a solution

I found the correct Q value of 5.594 MeV for part a. But for part b, I found the number of 238 Pu nuclei in a 1.0 g sample to be 1.433x10^26. I reason that there is 5.594 MeV of energy per nuclei, for a total of 8.0165x10^26 MeV total available energy in the sample. The answer is supposed to be in Watts, so I think I need to find the time interval over which the 8x10^26 MeV of energy is released (and convert the MeV to J!). That's why the half life is given, yet I am unsure on how to proceed to getting a time interval. Any help would be greatly appreciated.

-Lee

2. Dec 3, 2014

### Bystander

You might want to double check your arithmetic to this point first.

3. Dec 3, 2014

### leehufford

Whoops. Looks like I inverted the grams per mole. Inverting back gives 2.529x10^21 nuclei, with a total energy of 1.418x10^22 MeV. Thanks for the catch. Any advice on the time aspect? Thanks again,

Lee

4. Dec 3, 2014

### Bystander

If you want power as a function of time, calculate decays per second and do your conversion. If you want an "average" power over some service life (say one or two half lives), calculate total decay over that time, calculate that time in seconds, divide, do the conversion.

Double check the question as well to see that it asks for "power" and not energy. I'm guessing "power." And the way it's written, it looks like it's asking for instantaneous power, dQ/dt, so you'll want to set up the decay rate for decays/s.

Good 'nuff?

5. Dec 3, 2014

### leehufford

Yes. You got me moving in the right direction. I reasoned that the word "could" in the original problem meant total power output. I simply multiplied (decays/sec) and (energy) to get energy/sec, converted to joules and got the correct answer (its in the back of the book) of 0.57 Watts. Thank you for your help!

Lee

Last edited: Dec 3, 2014
6. Dec 16, 2015