Fermi Questions C

Test your knowledge of various Science Olympiad events.
User avatar
Name
Member
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

Re: Fermi Questions C

Postby Name » April 25th, 2018, 5:33 pm

Adi1008 wrote:
Name wrote:
Adi1008 wrote:How far does an air molecule (assume at STP) travel on average before it hits another air molecule, in meters?

Attempt
22 liters in a mole 6E23/22 is 3E22. Assuming a 1 dimentional movement the cube root of 3E22 is about 7E7. Because a liter is 1/10 of a meter, 7E8 air molecules in a straight line 1 meter. 1/7E8 is around E-9 so -9


Answer?
I saw both mentiones of -9 and -7 as a answer (3 nm and 68). I think it might be 68 but I can't understand the math behind it. Can you confirm what the answer is?

I believe that it would be , where is the number density and is the cross sectional area of an air molecule (going to make the rough assumption that diatomic oxygen and nitrogen have relatively similar sizes).

is about (you can calculate this using the Ideal Gas Law if you don't have it memorized). The cross sectional area of diatomic oxygen or nitrogen is about .

Doing the calculation would give a fermi answer of about -7.



Ok thanks! Also oops forgot to set up a question

Lets say you gained the ability to harvest salt from the ocean on a mass scale. If you take the salt and compacted it into a 1 meter radius sphere, what is it's escape velocity
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights
mit- 1st code, 3rd fermi
cornell- 1st fermi
states- 1st fermi, 3rd astro, 3rd code
19 medals

User avatar
Adi1008
Moderator
Moderator
Posts: 446
Joined: December 6th, 2013, 1:56 pm
Division: Grad
State: TX
Location: Austin, Texas

Re: Fermi Questions C

Postby Adi1008 » April 28th, 2018, 1:12 pm

Name wrote:
Adi1008 wrote:
Name wrote:
Attempt
22 liters in a mole 6E23/22 is 3E22. Assuming a 1 dimentional movement the cube root of 3E22 is about 7E7. Because a liter is 1/10 of a meter, 7E8 air molecules in a straight line 1 meter. 1/7E8 is around E-9 so -9


Answer?
I saw both mentiones of -9 and -7 as a answer (3 nm and 68). I think it might be 68 but I can't understand the math behind it. Can you confirm what the answer is?

I believe that it would be , where is the number density and is the cross sectional area of an air molecule (going to make the rough assumption that diatomic oxygen and nitrogen have relatively similar sizes).

is about (you can calculate this using the Ideal Gas Law if you don't have it memorized). The cross sectional area of diatomic oxygen or nitrogen is about .

Doing the calculation would give a fermi answer of about -7.



Ok thanks! Also oops forgot to set up a question

Lets say you gained the ability to harvest salt from the ocean on a mass scale. If you take the salt and compacted it into a 1 meter radius sphere, what is it's escape velocity

My (very rough) attempt
Volume of the oceans is about 18, so the mass is about 21. Guess that 1% of the ocean's mass is salt, so the salt mass is 19. Escape velocity is sqrt(2GM/r). G is -10, M is 19, r is 1. Escape velocity would be 4.

Actual answer
According to this reddit post, there's about 4.9 x 10^22 grams of salt = 4.9 x 10^19 kg of salt. Wolfram Alpha gives an answer of 5 overall.

How many complete rotations has the fastest pulsar made in the time between the extinction of the dinosaurs and the birth of Newton?
University of Texas at Austin '22
Seven Lakes High School '18
Beckendorff Junior High '14

User avatar
whythelongface
Exalted Member
Exalted Member
Posts: 326
Joined: March 12th, 2017, 7:42 pm
Division: Grad
State: NJ
Location: 705 kilometers overhead

Re: Fermi Questions C

Postby whythelongface » April 28th, 2018, 2:59 pm

Adi1008 wrote:How many complete rotations has the fastest pulsar made in the time between the extinction of the dinosaurs and the birth of Newton?

Attempt
The number of years between Newton's death and the present is negligible compared to the K-T extinction event, 65 mya (I think: this could just be one of those numbers the public loves to misquote). 7E7 years = what, 1 to 2E15 seconds?

I have no idea how many rotations a fast pulsar makes per second, but I think 40 rps was a number I encountered somewhere for pulsars? So my final answer is 17.


Answer
PSR J1748-2446ad spins at 716 hz. My K-T extinction estimate was correct, so my answer is off by a magnitude from the real answer, 18.

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?
WEST WINDSOR-PLAINSBORO HIGH SCHOOL SOUTH '18
EMORY UNIVERSITY '22
SONT 2017 5th Place Medalist [Microbe Mission]

"One little Sciolyer left all alone,
He went out and hanged himself and then there were none."

Congratulations to WW-P South for winning 14th place at Nationals!

User avatar
Name
Member
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

Re: Fermi Questions C

Postby Name » April 28th, 2018, 3:36 pm

whythelongface wrote: 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?


Really bad attempt
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?

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*
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights
mit- 1st code, 3rd fermi
cornell- 1st fermi
states- 1st fermi, 3rd astro, 3rd code
19 medals

User avatar
whythelongface
Exalted Member
Exalted Member
Posts: 326
Joined: March 12th, 2017, 7:42 pm
Division: Grad
State: NJ
Location: 705 kilometers overhead

Re: Fermi Questions C

Postby whythelongface » April 28th, 2018, 4:36 pm

Name wrote:
whythelongface wrote: 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?


Really bad attempt
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.
WEST WINDSOR-PLAINSBORO HIGH SCHOOL SOUTH '18
EMORY UNIVERSITY '22
SONT 2017 5th Place Medalist [Microbe Mission]

"One little Sciolyer left all alone,
He went out and hanged himself and then there were none."

Congratulations to WW-P South for winning 14th place at Nationals!

User avatar
Name
Member
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

Re: Fermi Questions C

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

whythelongface wrote:
Name wrote:
whythelongface wrote: 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?


Really bad attempt
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
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights
mit- 1st code, 3rd fermi
cornell- 1st fermi
states- 1st fermi, 3rd astro, 3rd code
19 medals

UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 1465
Joined: January 18th, 2015, 7:42 am
Division: C
State: PA

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?

User avatar
Name
Member
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

Re: Fermi Questions C

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

UTF-8 U+6211 U+662F wrote:Well, might as well prep for next year.

How many leaves are in Manhattan?


Attempt
2E5 leaves per tree and maybe E5 trees in Manhattan so E10


Answer
It says 5 million trees in NYC with 8 percent in Manhattan so 4E5 trees in Manhattan so actually E11


Name wrote: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*


Answer
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
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights
mit- 1st code, 3rd fermi
cornell- 1st fermi
states- 1st fermi, 3rd astro, 3rd code
19 medals

UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 1465
Joined: January 18th, 2015, 7:42 am
Division: C
State: PA

Re: Fermi Questions C

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

But sound can't travel in space :?

Attempt
Electrostatic force is approximately 10^10 * 10^-20 * 10^-20 and gravitational is approximately 10^-6 * 10^-26 * 10^-30, dividing gives 10^32


Answer
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.

User avatar
Unome
Moderator
Moderator
Posts: 4037
Joined: January 26th, 2014, 12:48 pm
Division: Grad
State: GA
Location: somewhere in the sciolyverse

Re: Fermi Questions C

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

Name wrote:By what magnitude is the electrostatic force of a eletron and proton greater then the gravitational force exerted from each other

Attempt
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.

Actual
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?
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.

UTF-8 U+6211 U+662F
Exalted Member
Exalted Member
Posts: 1465
Joined: January 18th, 2015, 7:42 am
Division: C
State: PA

Re: Fermi Questions C

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

Unome wrote:How many electrons flow through an iPhone 8 over the course of one battery charge?

Attempt
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


Answer
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

User avatar
Name
Member
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

Re: Fermi Questions C

Postby Name » May 1st, 2018, 1:27 pm

UTF-8 U+6211 U+662F wrote: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)


Attempt
Maybe around 6E3 km to Spain and 100 meter per Titanic so E5


Answer
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
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights
mit- 1st code, 3rd fermi
cornell- 1st fermi
states- 1st fermi, 3rd astro, 3rd code
19 medals

User avatar
TheChiScientist
Member
Member
Posts: 649
Joined: March 11th, 2018, 11:25 am
Division: Grad
State: IL
Location: Hiding from the college bounty hunters.

Re: Fermi Questions C

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

Attempt
Titanic was about a .1mile is so then if Spain to Maine is about 4,000 Miles? It would be 4x10^4


Answer
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!
A Science Olympian from 2015 - 2019
Medal Count:30 8-)
Background In
Boomilever,Code Busters,Exp Design, Thermo, WIDI, Hovercraft, Bridges, Wright Stuff, Geocaching, Fermi

School:Crystal Lake Central High School Wiki
Assassinator #119 and Co-Conspirator in #120
President of The Builder Cult. Builders rise up!

User avatar
Name
Member
Member
Posts: 275
Joined: January 21st, 2018, 4:41 pm
Division: C
State: NY
Location: Syosset

Re: Fermi Questions C

Postby Name » May 1st, 2018, 1:48 pm

TheChiScientist wrote:
Attempt
Titanic was about a .1mile is so then if Spain to Maine is about 4,000 Miles? It would be 4x10^4


Answer
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
South Woods MS (5 medals)/Syosset HS (24 medals)
Favorite Past Events: Microbe, Invasive, Matsci, Fermi
Next Year: Astro, Code, hopefully Orni, and maybe Compound
2018-19 highlights
mit- 1st code, 3rd fermi
cornell- 1st fermi
states- 1st fermi, 3rd astro, 3rd code
19 medals

User avatar
Unome
Moderator
Moderator
Posts: 4037
Joined: January 26th, 2014, 12:48 pm
Division: Grad
State: GA
Location: somewhere in the sciolyverse

Re: Fermi Questions C

Postby Unome » May 2nd, 2018, 6:43 am

Attempt
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

Answer
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.
Userpage
Chattahoochee High School Class of 2018
Georgia Tech Class of 2022

Opinions expressed on this site are not official; the only place for official rules changes and FAQs is soinc.org.


Return to “2018 Question Marathons”

Who is online

Users browsing this forum: No registered users and 2 guests