# Nuclear power homework

1. Jan 5, 2012

### Fixxxer125

1. The problem statement, all variables and given/known data
The $\alpha$ decay 238Pu →234U + $\alpha$releases 5.49 MeV energy. By a radio-thermal generator the decay energy is converted into electricity with an efficiency of 6.8%. The Voyager 2 spacecraft used such a nuclear battery. It was launched on 20.8.1977 and reached Neptune at 24.8.1989.
By which fraction was the electrical power diminished since launch?
By which fraction would the power from a solar panel have diminished in the
same period (distance Sun-Neptune = 30.1 AU)?
($\tau$ (238 Pu) = 127.16 years
2. Relevant equations
A(t)=A(0)exp(-T/$\tau$)

3. The attempt at a solution
I think I can calculate by what fraction of the electrical power the battery has decreased since launch. If the initial activity is A(0) then in 12 years the activity should have decreased by a factor of exp(-T/$\tau$) so will be 91% of the initial level. Thus the electrical power output will have decreased by around 1/10th. However I am not sure how the power from a solar panel would change over time. Many thanks

2. Jan 5, 2012

### Dick

The energy available from the solar battery is decreased at least by the amount the flux of energy from the sun is decreased by moving from 1 AU to 30.1 AU. Use the inverse square law.

3. Jan 6, 2012

### Fixxxer125

Thanks I'll give it a go!