I'll just go ahead and say it. Bananas are AWESOME. Maybe you like the taste and maybe you think they are disgusting. This has very little impact on the awesomeness of bananas. Why? Well, first there is the obvious nutritional value. Maybe this is so obvious that I will not talk about this aspect.
Bananas Are Clones
This doesn't have much to do with physics, but it's still cool. Wild bananas are apparently terrible. They have seeds in them and aren't as tasty as YOUR banana (which is also MY banana). Without seeds, bananas can't reproduce. To fix this, humans just take a part of an existing banana plant and replant it. BOOM. You get more bananas. Cloned bananas.
Ok, I am going to stop talking about banana clones before I say something that is just plain wrong (I might have already committed such a wrongness).
Bananas Are Radioactive
Radioactive isn't such a bad word. Really, lots of stuff is radioactive. This means that there is some type of nuclear reaction going on in the banana. In this case it is due to the potassium. Ok, before I go too far let me give you a link. This site has a pretty good description of the radioactive decay of potassium. I will assume the numbers listed are accurate.
Instead of going into all of the details, let me just list some important things from the previous link.
- Most of the potassium in a banana is 39K - 19 protons and 20 neutrons. This is stable.
- A very small fraction of the potassium is 40K. This is radioactive.
- There are three possible ways the 40K can decay. It could have a beta decay and turn into 40Ca. It could turn into 40Ar through electron capture - OR it could emit a positron and also turn into 40Ar.
- Although most of the potassium is not radioactive and most of the radioactive stuff just creates electrons, sometimes it will make a positron.
- For an average banana, it will (on average) produce 1 positron every 75 minutes.
Just to be clear, a positron is a type of antimatter. It is the antimatter version of the electron. Yes, antimatter. Just like in Star Trek. This is the other thing that makes bananas cool. Let me review: bananas are clones, bananas are radioactive and bananas produce antimatter. Three cool things.
What Can You Do With an Antimatter-Producing Banana?
Here is what I would do. I would make an antimatter based generator to power my house. Could I do that? I think so. The real question to consider: how many bananas would I need to produce 2000 watts.
As usual, I will start with some assumptions.
- Like I said above, a banana on average produces 1 positron every 75 minutes.
- This positron will annihilate in 10 cm of water (suppose I surround the banana with water).
- 50% of the energy from this positron-electron annihilation will go into increasing the thermal energy of the water.
- The efficiency of the turbine-generator is also 50%. I'm just estimating here. Don't get all upset.
- I am assuming the energy from the beta decay and electron capture don't matter. Maybe they really do matter, but antimatter energy is cooler.
How will this actually work? Here is my plan. I should patent this.
The bananas make positrons that annihilate with electrons in the water. This heats up the water and makes steam. The steam is then fed into a normal steam turbine generator (like in a gas or nuclear power plant). It's so crazy it just might work. Right?
But how many bananas do I need? Let's start with the average power of one banana. In 75 minutes, this average banana makes one positron. When the positron annihilates with an electron, we get energy from the mass-energy relationship E = mc2. Both the electron and positron have a mass of 9.11 x 10-31 kg. The speed of light is 3.00 x 108 m/s. This gives:
Assuming 50% energy goes to the water and then 50% of this goes into actual electricity, I get a power (from one banana) of:
Clearly, I need more than one banana. I need n bananas to get to 2000 Watts. What is n?
Ok. That is a lot of bananas. How big would my banana generator actually be? Let me just make some estimates. Say that an average banana is 150 grams (0.15 kg) with a density of about 1 g/cm3 (1000 kg/m3). The mass of all these bananas would be (0.15 kg)(n) = 3.3 x 1019 kg. With the density, I can calculate the volume of all these bananas.
I will choose to make my banana generator spherical. How big will this sphere of bananas be?
With my calculated volume, this would be a giant ball with a radius of 2 x 105 meters. Here is just the banana part of my banana powered generator as seen from space.
Maybe this wasn't such a good idea. I really doubt there are enough bananas on the whole Earth to build my generator. Maybe I would be better off using the bananas to feed some monkeys and have a monkey-powered generator.
Homework
I should always include homework with these type of posts.
- If you took my banana generator and spread the bananas over the Earth, how thick would it be? What if you just spread it over the land? How thick would this be in that case?
- I said I wanted 10 cm of water around my bananas. What mass and volume of water would this require?
- Suppose I used my banana generator on a trip to Mars. What would the gravitational field be on the surface of my spherical banana generator?
- Estimate the number of monkeys I would need to get 2,000 Watts of power from them. How many bananas would they need a day?
This isn't your traditional homework - in case you can't tell. If you want to use Google, I say go for it. Hopefully, Google won't give you the answer - but maybe it will give you a few important pieces of data that you can use.
