How Many Bananas to Power a Light Bulb?

[JohnCarter]

Homework Statement

If all of the energy from decay of the 40-K in one banana could be captured and converted into electrical energy, how many bananas would be needed to power a 100 W light bulb?

There is 358 mg potassium-K per 100 grams of banana

half life of potassium-40 is 1.248(3)×109 y

Homework Equations

ln(A/Ao)=-kt
e=mc2
k= (0.693/half-life)

The Attempt at a Solution

If a banana weighs 125 grams on average then there is 447.5 grams of potassium-40 in one banana.

(358)(1.25) = 447.5g
- - - - - - - - - - - - - -
k=(0.693/1.248(3)×10^9 y) = 5.55×10^-10

ln(A/Ao)=-kt
k = 5.55×10^-10
Ao = 447.5 g
t=?

 

[NascentOxygen]

That's 447.5 mg of K-40

You'll need an equation that includes the energy of decay of the isotope.