> 15 decays per second from one banana work out to a couple of picowatts of power, roughly the power consumption of a single human cell. Even if you captured that decay energy with perfect efficiency, powering a house would require about 300 quadrillion[6] bananas
> [6] Fine, I looked it up this time.
I think that's out by a factor of 1000.
Potassium-40 decays 89.28% of the time to calcium-40, releasing 1.31 MeV, and 10.72% of the time to argon-40 releasing 1.46 MeV [1]. That's .8928*1.31+.1072*1.46 = 1.32608 MeV per decay on average, which is about 2.1246e-13 Joules [2] per decay on average. 15 decays per second is 15*2.1246e-13 ≈ 3.1869e-12 Watts = 3.1869 picowatts per banana. I think Randall is using 1000 Watts as the average power usage of a house. 1000/3.1869e-12 ≈ 3.1378e14 ≈ 300,000,000,000,000 = 300 trillion bananas. Maybe he looked it up wrong?
Can anyone confirm this?
I can't find the packing density of bananas, but if it was 1000 kg/m^3, a medium banana is ~118 g [3], so 1000/.118 ≈ 8475 bananas / cubic metre, so 300e14/8475 ≈ 3.54e12 cubic metres of bananas. The New York metro area is about 12000 km^2 = 12e9 m^2 [4], so the depth of the banana pile is on average 3.54e12/12e9 ≈ 295 metres, which is indeed taller than most of the buildings, so that bit seems right.
It's half past midnight here, so I'm well into "Someone is wrong on the internet" [5] territory....
> [6] Fine, I looked it up this time.
I think that's out by a factor of 1000.
Potassium-40 decays 89.28% of the time to calcium-40, releasing 1.31 MeV, and 10.72% of the time to argon-40 releasing 1.46 MeV [1]. That's .8928*1.31+.1072*1.46 = 1.32608 MeV per decay on average, which is about 2.1246e-13 Joules [2] per decay on average. 15 decays per second is 15*2.1246e-13 ≈ 3.1869e-12 Watts = 3.1869 picowatts per banana. I think Randall is using 1000 Watts as the average power usage of a house. 1000/3.1869e-12 ≈ 3.1378e14 ≈ 300,000,000,000,000 = 300 trillion bananas. Maybe he looked it up wrong?
Can anyone confirm this?
I can't find the packing density of bananas, but if it was 1000 kg/m^3, a medium banana is ~118 g [3], so 1000/.118 ≈ 8475 bananas / cubic metre, so 300e14/8475 ≈ 3.54e12 cubic metres of bananas. The New York metro area is about 12000 km^2 = 12e9 m^2 [4], so the depth of the banana pile is on average 3.54e12/12e9 ≈ 295 metres, which is indeed taller than most of the buildings, so that bit seems right.
It's half past midnight here, so I'm well into "Someone is wrong on the internet" [5] territory....
[1] https://en.wikipedia.org/wiki/Potassium-40
[2] https://www.unitjuggler.com/convert-energy-from-MeV-to-J.htm...
[3] https://www.healthline.com/nutrition/bananas-calories-carbs
[4] https://en.wikipedia.org/wiki/New_York_metropolitan_area
[5] https://xkcd.com/386/