Power produced from alpha decay

[MattHorbacz]

Homework Statement

Assume that a 14 kg sample of 240Pu is used to produce electrical power from its α decay. If your device is 60% efficient in producing electrical power, how much power can be produced? (in watts)

Homework Equations

Q=mass of plutonium-mass alpha-mass daughter; 240 plutonium= alpha +uranium236

The Attempt at a Solution

I found Q to be 5.25572 Mev. The number of Plutonium atoms is 14*10^3 grams * 6.022*10^23/240. Multiply this by Q to get total energy in ev. Then multiply by 1.602176565e-19 to get in terms of Joules. Then multiply by .6, and that's where I get stuck. No idea how to get to watts. the answer should be 59.4 watts.

 

[SteamKing]

Homework Statement

Assume that a 14 kg sample of 240Pu is used to produce electrical power from its α decay. If your device is 60% efficient in producing electrical power, how much power can be produced? (in watts)

Homework Equations

Q=mass of plutonium-mass alpha-mass daughter; 240 plutonium= alpha +uranium236

The Attempt at a Solution

I found Q to be 5.25572 Mev. The number of Plutonium atoms is 14*10^3 grams * 6.022*10^23/240. Multiply this by Q to get total energy in ev. Then multiply by 1.602176565e-19 to get in terms of Joules. Then multiply by .6, and that's where I get stuck. No idea how to get to watts. the answer should be 59.4 watts.

You need to know how quickly Pu-240 decays. Do you know the half-life of Pu-240?

 

[MattHorbacz]

I looked it up at it seems to be about 6560 years

 

[SteamKing]

I looked it up at it seems to be about 6560 years

OK, from that, you need to figure out how many atoms of Pu-240 are decaying each second in your original 14 kg of this substance.

Knowing that, you have already computed how much energy is released with each decay, so finding the power should be trivial.