Fermi Quiz . Aim: To estimate the values of various quantities. Materials: None - except an imaginative, innovative mind. Method: For questions #1 ⇒ #13, provide the power of 10 that best answers the question.

For question #14, your answer is just a number (not a power of 10). Question #15 will be a tiebreaker and will not be scored unless there is a tie.

Conditions: The answers must be entered using the units specified. WRITE CLEARLY! Ranking: Each question’s score will be the difference between the correct answer and your

answer. A penalty applies for leaving answers blank, so take your best guess if you can’t calculate an answer.

Team Name ________________  

1) If  all  the  rain  that  falls  during  a  typical  summer  rainstorm  were  gathered  into  a  single  drop,  what  would  the  drop’s  radius  be?  

Answer:  10                    meters  

2) When  a  large  ship  (oil  tanker  /  cargo  ship  /  aircraft  carrier  /  etc.)  is  placed  into  the  ocean,  how  much  does  the  global  sea  level  rise?  

Answer:  10                    meters  

3) Archimedes  of  Syracuse  was  a  philosopher,  inventor,  and  scientist  who  lived  and  died  in  Sicily  more  than  2,000    years  ago.  Assuming  that  the  earth’s  atmosphere  has  been  thoroughly  mixed  since  then,  how  many  molecules  from  his  final  breath  are  in  your  lungs  right  now?  

Answer:  10                    molecules  

4) How  many  airline  passengers  are  in  the  air  over  the  United  States  right  now?  

Answer:  10                      passengers  

5) What  is  the  kinetic  energy  stored  in  continental  drift?  

Answer:  10                      Joules  

6) What  is  the  kinetic  energy  stored  in  all  the  wind  in  the  Earth’s  atmosphere?  The  specific  gravity  of  air  is  1/1000th  that  of  water.  You  should  only  consider  the  atmosphere’s  motion  relative  to  the  surface  of  the  Earth,  and  not  the  overall  rotation  of  the  planet.  

Answer:  10                      Joules  

7) Sunlight  exerts  a  force  of  1  micronewton  per  square  meter.  Ignoring  friction,  how  long  would  it  take  a  car  powered  by  this  force  to  go  from  0  mph  to  60  mph  (or,  equivalently,  from  0  kph  to  100  kph)?  

Answer:  10                      seconds  

8) How  many  babies  are  born  in  New  Haven  on  an  average  day?  

Answer:  10                      babies  per  day  

9) How  many  trees  are  there  in  Connecticut?  

Answer:  10                      trees  

10) Despite  what  you  may  have  learned  in  chemistry  class,  any  pair  of  atoms  will  stick  to  each  other  to  form  a  diatomic  molecule.  Given  this  fact,  how  many  species  of  diatomic  molecules  are  there?  

Answer:  10                      species  

11) You  have  a  one-­‐liter  bottle  of  water.  What  is  the  area  you  could  cover  with  this  water  if  it  were  spread  to  be  one  molecule  thick?  

Answer:  10                      square  meters  

12) How  long  a  line  can  an  average  pencil  make?  

Answer:  10                      meters  

13) If  all  the  soda  that  is  drunk  in  the  United  States  during  a  typical  day  were  gathered  into  a  single  drop,  what  would  the  drop’s  radius  be?  

Answer:  10                      meters  

14) How  many  generations  back  do  you  have  to  go  until  your  total  number  of  ancestors  is  equal  to  the  world  population?  (note:  this  is  the  only  question  where  you  should  just  give  a  number,  rather  than  an  exponent).      

Answer:                      Generations  

15) TIEBREAKER  If  electric  energy  costs  $0.1  per  kilowatt  hour,  and  is  delivered  to  your  home  at  a  voltage  of  120  Volts,  what  is  the  cost  of  one  electron?  Note  that  the  charge  of  an  electron  is  1.6  x  1019  Coulombs,  and  the  power  delivered  by  electric  flow  is  equal  to  the  voltage  times  the  current.  

Answer:  10                    dollars

Solutions  to  Fermi  Quiz,  

1) If  all  the  rain  that  falls  during  a  typical  summer  rainstorm  were  gathered  into  a  single  drop,  what  would  the  drop’s  radius  be?  

Typical rainfall in a rainstorm is 1 cm. Typical spatial extent of a rainstorm (based on familiar images of weather radar from TV weather reports) is 100 km x 100 km. Total volume is 108 cubic meters. Radius is cube root of this, 52 meters. So round the 5 up to 10, answer is +3.

2) When  a  large  ship  (oil  tanker  /  cargo  ship  /  aircraft  carrier  /  etc.)  is  placed  into  the  ocean,  how  much  does  the  global  sea  level  rise?  

Large ship draws 1,000 feet by 100 feet by 100 feet = 107 cubic feet = 3x105 m3. The surface area of the earth is 4 Pi (8,000 km2) = 8x108 km2 = 8x1014m2. Spreading 3x105 m3 over 8x1014m2 gives 4x10-10 m. So answer is -10

3) Archimedes  of  Syracuse  was  a  philosopher,  inventor,  and  scientist  who  lived  and  died  in  Sicily  more  than  2,000    years  ago.  Assuming  that  the  earth’s  atmosphere  has  been  thoroughly  mixed  since  then,  how  many  molecules  from  his  final  breath  are  in  your  lungs  right  now?  

22.4 liters = 1 mole = 6x1023 molecules. Typical breath = 1 liter = 3x1022 molecules in Archimedes’ last breath.

Volume of earth’s atmosphere = 8x1014 m2 (area of earth, see last question) * 30 km (mean height of atmosphere) = 2.4x1018 m3 = 2.4x1021 liters. So 10 of Archimedes’ last molecules are in each liter of the atmosphere.

Your lungs now hold roughly one liter. So there should be (on average) 10 of Archimedes’ last molecules in your lungs now.

So answer is: +1

4) How  many  airline  passengers  are  in  the  air  over  the  United  States  right  now?  

Average person in America flies 10 times per year, so 3x109 passengers per year, so 1x107 passengers per day. Average flight is 3 hours so 1.3x106 passengers in the sky at a time.

So answer is +6

5) What  is  the  kinetic  energy  stored  in  continental  drift?  

For mass, use density = 5x103 kg/m3. Area 1x107 km2, thickness = 10 km gives volume = 1x1017 m3, so mass = 5x1020 kg. Velocity = 1 cm/yr = 1x10-2 m / 3x107s = 3x10-10 m/s. So ½ mv2 is 50 Joules.

So answer is +2

6) What  is  the  kinetic  energy  stored  in  all  the  wind  in  the  Earth’s  atmosphere?  The  specific  gravity  of  air  is  1/1000th  that  of  water.  You  should  only  consider  the  atmosphere’s  motion  relative  to  the  surface  of  the  Earth,  and  not  the  overall  rotation  of  the  planet.  

Volume of air is 2.4x1018 m3 (see problem 4). Density is 1 kg/m^3, so mass of atmosphere is 2.4x1018 kg. A typical wind speed is 100 km/h = 30 m/s. So ½ mv2 is 10x1020 Joules.

So answer is +20

7) Sunlight  exerts  a  force  of  1  micronewton  per  square  meter.  Ignoring  friction,  how  long  would  it  take  a  car  powered  by  this  force  to  go  from  0  mph  to  60  mph  (or,  equivalently,  from  0  kph  to  100  kph)?  

Car area = 1 m2 gives 1x10-6 Newton. Car mass = 1x103 kg, so acceleration = 1x10-9 m/s2. 100 kph = 30 m/s, so it would take 3x1010 seconds.

So answer is +10.5

8) How  many  babies  are  born  in  New  Haven  on  an  average  day?  

Population = 1x105. Life expectancy = 75 years. For constant population growth (ignoring immigration), assume one birth per person per 75 years. Gives 1300 births per year = 4 births per day.

So answer is +1

9) How  many  trees  are  there  in  Connecticut?  

Google Maps satellite image of CT looks like it is about half forested. CT is 100 km x 100 km = 1x104 km2 = 1x1010 m2 or 5x109 m2 of trees. Assume trees are 10 m apart, 100 m2 per tree gives 5x107 trees in CT.

So answer is +7

10) Despite  what  you  may  have  learned  in  chemistry  class,  any  pair  of  atoms  will  stick  to  each  other  to  form  a  diatomic  molecule.  Given  this  fact,  how  many  species  of  diatomic  molecules  are  there?  

Roughly 100 atomic species, so 10,000 diatomic molecules.

So answer is +2.

11) You  have  a  one-­‐liter  bottle  of  water.  What  is  the  area  you  could  cover  with  this  water  if  it  were  spread  to  be  one  molecule  thick?  

One liter = 1x10-3 m3. One molecule = 1x10-10 m. So area would be 1x107 m2.

So answer is +7.

12) How  long  a  line  can  an  average  pencil  make?  

Assume pencil marking is 100 nm thick and 1 mm wide. Pencil graphite is 1 mm thick and 100 mm long = 1x10-7 m3. This gives length 1x103 m.

So answer is +3.

13) If  all  the  soda  that  is  drunk  in  the  United  States  during  a  typical  day  were  gathered  into  a  single  drop,  what  would  the  drop’s  radius  be?  

Average person drinks one can: 3x108 people x 0.3 liters = 1x108 liters = 1x105 m3, drop radius is 50 meters. So answer is +2

14) How  many  generations  back  do  you  have  to  go  until  your  total  number  of  ancestors  is  equal  to  the  world  population?  (note:  this  is  the  only  question  where  you  should  just  give  a  number,  rather  than  an  exponent).      

Present world population is 7x109. 30 generations gives 1x109 ancestors; 25 years per generation puts this 750 years ago. World population in 1250 AD was about 1x109.

So answer is +30

15) TIEBREAKER  If  electric  energy  costs  $0.1  per  kilowatt  hour,  and  is  delivered  to  your  home  at  a  voltage  of  120  Volts,  what  is  the  cost  of  one  electron?  Note  that  the  charge  of  an  electron  is  1.6  x  1019  Coulombs,  and  the  power  delivered  by  electric  flow  is  equal  to  the  voltage  times  the  current.  

P = I V E = I V t = C V If C = 1.6x10-19 Coulombs and V = 120 Volts, then the energy of one electron is 2x10-17 Joules = 2x10-17 Watt Second = 2x10-20 kW second = 7x10-24 kW hr = 7x10-25 Dollars.

So answer is: -24