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Hardest question ever

  1. Jan 6, 2004 #1
    my teacher couldent even get the answer to this multiple choice question....could anyone at least attempt this thank you

    For each breath that you take, how many of the air molecules would also been breathed by the patron saint of Physics, Sir Isaac Newton (1642-1727)during his life time, the atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 3.33*10^-9 m along a side, the earths radius is 6..38*10^6. make any reasonable assumptions for any data needed.

    a) 6 b) 6*10^3 c) 6*10^6 d) 6*10^9 e) 6*10^12
  2. jcsd
  3. Jan 6, 2004 #2


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    Boy that's a stupid question.

    I'd first find out how many atoms (according to the information given) there are in the atmosphere, then find out how many days Newton lived, approximate how many breaths the average person makes in a day, and make the (very bad) assumption that you breathe different molecules each time. Assuming that a breath is about half a liter, you can guesstimate the percentage of molecules which Newton breathed in his lifetime.

    You then have the fraction of each breath which was breathed by Newton (assuming perfect mixing).

    I'm sure someone else will have a different take on it.

    Lame question...
  4. Jan 6, 2004 #3
    hmm...first of all it isent my question...its of the SIN test from the 2003 university of waterloo physics exam.

    if u cant get the answer, u shouldent of replied...

    am just curious of how to do it..so if anyone out there knows, i'd appreiciate it if u answerd this
  5. Jan 6, 2004 #4
    What a stupid thing to say. Enigma gave you a decent roadmap so that you could solve it yourself. Instead of b!tching, you might try "thank you."
  6. Jan 6, 2004 #5
    Woah, settle down, guys. We don't need a virtual fight going on. Decibel, if a guy gives you some help, don't get really angry. Like you said, it was a hard question. A guy was throwing out some ideas on how to solve it. Every little bit helps.
  7. Jan 6, 2004 #6
    well i dident mean it that way....he says "boy" then says whata stupid question, that kind of implies an insult to me...even though i dident think of the question....and i cant solve it myself cause am not as expeirenced in physics as some of the ppl here, and that is the reason i posted this in a forum
  8. Jan 6, 2004 #7
    Newton had bad breath.

  9. Jan 6, 2004 #8


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    No insult intended to you! The person who wrote the question maybe, but certainly not you!

    That's the problem with internet forums. You can't necessarily tell when a comment is dripping sarcasm.


    Sorry for any miscommunications. I was merely commenting that the problem, as stated, is impossible to solve unless you make mad-crazy assumptions, many of which are absolutely invalid in real life (like you can see from my parenthesis in the above post). Therefore, since the problem is so whacked, any answers you may get are equally whacked. Therefore, it's a stupid question for them to ask you.

    EDIT: Now that I think about it, it probably isn't a question where the answer matters, it's the steps you took to solve the problem that they care about. It's like in a job interview (for example) where they ask you on the spot: "How many quarters stacked end to end would be as tall as the Empire State Building?" They don't know the answer to the question, and they don't care. They want to see you go: "OK, a quarter is about a quarter inch long, so 4 would fit in an inch or 48 to a foot. The ESB I'm guessing is 100 stories, and I'll guess 10 feet to a story, therefore about 48,000 quarters." Whether you're in the right ballpark doesn't matter.
    Last edited: Jan 7, 2004
  10. Jan 7, 2004 #9
    k well ur right enigma lots of assumptions but heres the answer

    This is a Fermi type of problem, and you must supply reasonable numbers to get a rough answer! Answers are 3 orders of magnitude apart, so you can even afford to be sloppy! If each breath of Sir Isaac's (and ours) is about 1 litre = 10-3 m3, and they are 3 seconds apart, then in 1727-1642=85 years, he will have had 85 x 365 x 24 x 3600 /3 = 8.93 x 108 breaths, for a total volume of 8.93 x 105 m3. We will assume that the air mixes well enough that we do not have to worry about air being breathed twice.

    The total volume of the atmosphere is 4 Re2 h, where Re is the Earth's radius, and h is the height of the atmosphere, giving 4.08 x 1018 m3. The fraction of air molecules ever breathed by the patron saint of Physics is thus 8.93 x 105 / 4.08 x 1018 = 2.19 x 10-13. The number of molecules in each breath of ours is the density 1/(3.3 x 10-9)3 = 2.78 x 1025 m-3, multiplied by the volume of each breath, 10-3 m3, or 2.78 x 1022 molecules. Multiplying by the fraction breathed by Newton, each breath of ours has about 6.08 x 109 molecules also breathed by him (D). Since we have about 9 x 108 breaths, each breath of ours has about 7 molecules also breathed by Isaac Newton.
  11. Mar 5, 2010 #10
    WOW! im impressed!
    you must have a headache now!
  12. Mar 5, 2010 #11


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    I wouldn't have thought you'd need so much working out for a multiple choice question, that would basically take alot of your short/long answer questions time away ;l
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