Fermi Questions C

Test your knowledge of various Science Olympiad events.
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Re: Fermi Questions C

Postby Name » April 28th, 2018, 4:53 pm

RuBisCO is the most abundant enzyme in the entire biosphere. RuBisCO fixes carbon dioxide into ribulose bisphosphate, but can also fix diatomic oxygen into RuBP in a wasteful process known as photorespiration. How many kilograms of O2 are metabolized by RuBisCO within the entire biosphere in one second?
RuBisCO I think is in the leaves. Trees make up the majority of leaves. There are about E12 trees. I have no idea how many RuBisCO are in a leaf. I'm gonna assume a tree uses 100 calories a day (thier large but don't spend energy moving and whatnot) so E14 calories of energy are used per day. There are 5 Cal of energy in a gram of glucose so 2E13 grams of glucose have to be produced. About 200 grams per mole 6E34 glucose molecules. I think it takes 6 cycles for 1 molecule (I suck at bio) so 6 o2 will be fixed or 3E35. Or 5E11 moles of 02 or about 2E10 grams of o2 or 2E7 kg per day or 2 per second.
Can't find anything on the answer, and my answer seems off. Can you confirm what the answer is?
I cannot confirm because I have not calculated it myself and am far too lazy to do so, but I'll give you some numbers:
"For every person on Earth, there are around five kilograms of RuBisCO in the biosphere."
"At ambient levels of carbon dioxide and oxygen, the ratio of the reactions is about 4 to 1, which results in a net carbon dioxide fixation of only 3.5."
I can't find the data for rate of carbon fixation, but if you really wanted to, you probably could.
I can't find the rate and really don't want to search more but the number is probably significantly higher then 2
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Re: Fermi Questions C

Postby UTF-8 U+6211 U+662F » April 29th, 2018, 7:02 pm

Well, might as well prep for next year.

How many leaves are in Manhattan?

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Re: Fermi Questions C

Postby Name » April 30th, 2018, 3:30 pm

Well, might as well prep for next year.

How many leaves are in Manhattan?
2E5 leaves per tree and maybe E5 trees in Manhattan so E10
It says 5 million trees in NYC with 8 percent in Manhattan so 4E5 trees in Manhattan so actually E11
At the current rate this thread is moving at (starting from the first post) how many posts will there be in the time it takes for sound to travel from here to Sagittarius A*
Distance to Sagittarius A is about E18 km or 21 m. Speed of sound about 300m/s so 3E18 seconds or E15 hour or 5E13 days. Post rate works out to about 1/day so 14 posts
By what magnitude is the electrostatic force of a eletron and proton greater then the gravitational force exerted from each other
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Re: Fermi Questions C

Postby UTF-8 U+6211 U+662F » May 1st, 2018, 12:16 pm

But sound can't travel in space :?
Electrostatic force is approximately 10^10 * 10^-20 * 10^-20 and gravitational is approximately 10^-6 * 10^-26 * 10^-30, dividing gives 10^32
Actually around 10^39 (whoops)
How many full-scale models of the Titanic would you have to lay to build a bridge across the Atlantic Ocean (from around Maine to Spain)

edit: Or Unome can post his answer before I finish editing whoops
Last edited by UTF-8 U+6211 U+662F on May 1st, 2018, 12:36 pm, edited 2 times in total.

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Re: Fermi Questions C

Postby Unome » May 1st, 2018, 12:26 pm

By what magnitude is the electrostatic force of a eletron and proton greater then the gravitational force exerted from each other
Assumed distance of 1 m for simplicity. Gravitational force = (6.7E-11)(1E-27)(2E-24) = ~1.2E-61. Electrical force = (9E9)(1.6E-19)(1.6E-19) = 2.7E-28. E/G = 2E33 so Fermi Answer: 33.
Confirmed the measurements via the internet, however I accidentally used grams instead of kg for the masses :oops:
How many electrons flow through an iPhone 8 over the course of one battery charge?
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Re: Fermi Questions C

Postby UTF-8 U+6211 U+662F » May 1st, 2018, 12:52 pm

How many electrons flow through an iPhone 8 over the course of one battery charge?
Suppose iPhone 8s charge for five hours (5*3600 or 18000 seconds). Suppose it's charging at around 100 amps. Then, 1E2*2E4*6E18 = 1E25 electrons
Turns out the iPhone 6 takes 2.9 hours with a 1A charger. Thus, 6.5E22 electrons are needed, rounding up to 23
See my previous post for the next question

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Re: Fermi Questions C

Postby Name » May 1st, 2018, 1:27 pm

How many full-scale models of the Titanic would you have to lay to build a bridge across the Atlantic Ocean (from around Maine to Spain)
Maybe around 6E3 km to Spain and 100 meter per Titanic so E5
So distance is actually 5E3 and length of Titanic is 300 meter so E4
If a supernova occered and spewed out all it's energy in the form of visible light photons, how many photons will it spew out
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Re: Fermi Questions C

Postby TheChiScientist » May 1st, 2018, 1:34 pm

Titanic was about a .1mile is so then if Spain to Maine is about 4,000 Miles? It would be 4x10^4
6 Titanics is equal to about a mile so then the distance of Spain to Maine is 3,249mi(Whoops) so then multiple 3,249 times 6 and tada! You get 19494 making the fermi answer 1.9x10^4 :)
Edit: Dang it Name!
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Re: Fermi Questions C

Postby Name » May 1st, 2018, 1:48 pm

Titanic was about a .1mile is so then if Spain to Maine is about 4,000 Miles? It would be 4x10^4
6 Titanics is equal to about a mile so then the distance of Spain to Maine is 3,249mi(Whoops) so then multiple 3,249 times 6 and tada! You get 19494 making the fermi answer 1.9x10^4 :)
Edit: Dang it Name!
Hey at least you got it right.
Quick advice, I feel like knowing numbers in SI units is easier, and convert when necessary. Using numbers in equations is usually SI units, and alotta conversations leaves more room for error.

Repost question:
If a supernova occered and spewed out all it's energy in the form of visible light photons, how many photons will it spew out
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Re: Fermi Questions C

Postby Unome » May 2nd, 2018, 6:43 am

Peak power emitted by a supernova is ~1E41 Watts - let's take this over a time of 3E1 days or so, giving us 3E47 Joules. Roughly, 1200 over wavelength in nm is energy in electronvolts, so visible light is around 1.2E3/5E2 = 2 eV per photon, which is ~3E-19 Joules per photon. Dividing the two values gives Fermi Answer: 66
I'll assume that you're referring to a core-collapse supernova, which produces approximately 1E46 Joules of energy. Visible light is probably best represented by the midpoint, 550 nm, which is equivalent to 2.254 eV, which is 3.612E-19 Joules per photon. Dividing yields: 2.7E64, so Fermi Answer: 64
How many times greater than the current value would the mass of the moon have to be in order to cause tides high enough to make Fort Collins, CO a coastal city at high tide? Assume uniform tides worldwide and ignore the effects of the increased mass on the oblateness of Earth.
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