western
Physics and Astronomy

                                   
 
Fermi Questions
Objective

A "Fermi question" is a question in physics which seeks a fast, rough estimate of quantity which is either difficult or impossible to measure directly.

For example: The question "How many drops of water are there in Lake Erie?" requires an estimate of the volume of a drop, the volume of Lake Erie from its approximate dimensions and conversion of units to yield an answer. This answer would be an estimate hopefully accurate within an order of magnitude, i.e. a factor of ten.

Purpose

The marking scheme for these questions is best explained by an example. Suppose that the question is "What is the mass of Lake Erie", and that the "correct" answer is 10^15 kg. (i.e. 10 raised to the fifteenth power)

An answer in the range:                   Mark

2 X 10^14 - 5 X 10^15                   5
4 X 10^13 - 2 X 10^16                   3
8 X 10^12 - 1 X 10^17                   1

All questions will be marked according to this general scheme, although, of course, the actual ranges will be wider or narrower, depending on the degree of difficulty in estimating the quantities involved.

After the answers have been marked, each team may be asked to give oral explanations of some of the answers, so you should be prepared for that.

Participants Team of up to six members.
Materials One envelope of Fermi Questions; pencils and paper.
Rules

1. Your school team will be seated around a table.
2. Teams will receive an envelope containing TEN (10) Fermi questions, each on a separate sheet for distribution to team members. Each sheet has space for working out the question, and at the bottom is a place for the answer, along with the units in which it must be given. Answers given in other units will get a mark of zero.
3. Teams will be given 12 minutes to answer as many questions as possible.
4. The group of team answers will be collected at the end of 12 minutes and points will be awarded for answers within given ranges.
There are purposely more questions than can be easily answered within this time limit. However you will answer more of them if you concentrate on estimating quantities, rather than trying to get them exactly.
5. Calculators are not allowed in this event.

Judging
Version 1

The marking scheme for these questions is best explained by an example. Suppose that the question is "What is the mass of Lake Erie", and that the judges' best estimate is 10^15 kg. (i.e. 10 raised to the fifteenth power)

An Answer within
a factor of

i.e.: an answer in the range:
  Mark
5
2 X 10^14 - 5 X 10^15
5
10
4 X 10^13 - 2 X 10^16
3
100
8 X 10^12 - 1 X 10^17
 1

All questions will be marked according to this general scheme, although the actual ranges will be wider or narrower, depending on the degree of difficulty in estimating the quantities involved.

Judging
Version 2

Teams are required to give a three-part answer (a) the minimum possible value (b) the best estimate (c) the maximum possible value.

Each of these components is scored separately according to the scheme given in Version 1 above

Example:

 
Minimum Value
Best Estimate
Maximum value
Total Score
Judges Answer
1x 10^15
Team Answer
1 x 10^15
8 x 10^15
2 x 10^16
Team Score
5
3
1
9

All questions will be marked according to this general scheme, although the actual ranges will be wider or narrower, depending on the degree of difficulty in estimating the quantities involved.

For one question only, you will be asked to give in addition: (a) your assumptions (b) your solution steps.

After the answers have been collected, each team may be asked to give oral explanations of some of the answers.

How to do Fermi Questions

Ryan Menzies has develpoed a new site for Fermi Questions: http://www.fermiquestions.com

Source: Columbia University

The Nobel-prize-winning physicist, Enrico Fermi, came up with this simple and intuitive way to deduce the circumference of the earth.
1. How many time zones do you pass through when you fly from New York to Los Angeles?
Answer, 3
2. How many miles is it, about, over that same distance?
Answer, about 3000.
3. How many miles per time zone, on average?
Answer, about 1000
4. How many time zones must there be around the world?
Answer, 24 because there are 24 hours in a day
5. How many miles around the world?
Answer, 24 time zones x 1000 miles per time zone = 24000 miles
Yes, it is about 24000 miles around the world.

So how do I get the diameter of the Earth

1. the formula for a circle is 2 pi r, right? where r is the radius and pi is about 3
2. so 24000 mi = 2 x 3 x r = 6 x r

3. therefore 24000 mi / 6 = r = 4000 mi

4. the diameter of the earth is 2 x r = 8000 mi, where the diameter is 2 times the radius

5. 1 mi = 1.6 km so 8000 mi x 1.6 km/mi = 12800 km

(the correct answer is ~12742 km)

So you can always figure out the dimensions from your basic knowledge of traveling!

Fermi Questions

1. How much has the mass of the human population on the earth increased in the last year? (kilograms)
2. If the mass of one teaspoon of water could be converted entirely into energy in the form of heat, what volume of water, initially at room temperature, could it bring to a boil? (litres).
3. How much does the Thames River heat up in going over the Fanshawe Dam? (Celsius degrees).
4. How much energy does a horse consume in its lifetime? (joules)
5. What is the weight of the air over Lake Superior? (Newtons)
6. How many joules of chemical energy are there in one litre of gasoline? (Joules)
7. How many bricks are there in (London)? (a number)
8. What is the mass of all the automobiles scrapped in North America this month? (kilograms)
9. How many air molecules in an automobile tire? (a number)
10. How many photons/sec are emitted by a 100 watt light bulb? (a number)
11. How long would it take a paramecium to swim from London to Toronto? (seconds)
12. How many cells are there in the human body? (a number)
13. How many oxygen molecules enter your lungs on each inhalation? (a number)
14. How many kilometres of D.N.A. are there in the cells of one human body? (kilometres)
15. How many dollars would each person on this planet possess if there were a "mole" of dollars to distribute? (a number)
16. How many meters would a ground state electron in a hydrogen atom be from its nucleus if the nucleus of the hydrogen atom was blown up to the size of a baseball? (metres)
17. How many water molecules are there in a totally filled olympic size swimming pool? (a number)
18. To what height could loose leaf paper be stacked if you possessed Avogadro's number of sheets? (metres)
19. How many years would it take for MacDonalds to sell a mole of their hamburgers? (years)
20. How many atoms of iron are there in a sewing needle? (a number)
21. How many litres of gasoline are used in your home town in one week? (litres)
22. How many electrons could a fully charged 12 volt car battery release before it was completely discharged? (a number)
23. How many gas molecules are there in the earth's atmosphere (a number)
24. How many sodium ions are in one tablespoon of salt? (a number)
25. What volume of hydrogen gas measured at S.T.P. could be produced by the electrolysis of all the water in Lake Erie? (litres)
26. When the island of Krakatoa was destroyed by a volcanic eruption, the sound waves could be detected world wide. How long would it take for such a wave to travel around the earth and come back to Krakatoa? (seconds)
27. If fighter pilots experience too high "gee" forces in a turn they black out. What is the minimum safe vertical turning circle for a plane travelling at the speed of sound? (metres)
28. Estimate the mass of lead deposited each year in London due to emissions from automobiles. Each litre of gas contains about 2 grams of lead. (kilograms)
29. How many piano tuners are there in Toronto? (a number)
30. How many electrons are there in the electron beam between the cathode of your T.V. set and the screen?
31. What is the thickness of this paper in wavelengths of visible light? (a number)
32. Calculate the gravitational attraction between a man and a woman as they stand talking to each other. (newtons)
33. A weather balloon is one metre in diameter and filled with helium. What is its diameter when taken to the bottom of the Atlantic Ocean? (metres)
34. There are approximately 1.5 x 10^9 cubic kilometres of ocean. If the water was to evaporate, what mass of minerals would remain behind? (kg)
35. People crowd into London until all available open space within the city limits is covered with standing people. How many people would there be? (a number)

Source: Richard K Curtis

36. How many golf balls will fit in a suitcase?
37. How many hairs are there on a human head?
38. How many individual frames are needed for a feature length motion picture?
39. What is the ratio of spacing between gas molecules to molecular diameter in a gas at standard temperature and pressure?
40. How many seconds are there in a year?
41. If your life earnings were doled out to you by the hour, how much is your time worth per hour?
42. What is the weight of solid garbage thrown away by American families each year?
43. How many molecules are in a standard classroom?


Source: Prof. L.B. Weinstein, Old Dominion University.


Physicists should be able to estimate the order-of-magnitude of anything. How many atoms of Julius Caesar do you eat every day? How much waste does a nuclear power plant generate?

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General Estimation (no physics required)


44. How many pieces of popcorn does it take to fill a room?
45. How many 1 gallon buckets of water are needed to empty Loch Ness?
46. How much dental floss does a prisoner need to escape over a wall?
47. What is the volume of human blood in the world? How does this compare to the volume of the valley at Har Meggido (Armaggedon)?
48. How fast does human hair grow (in km/hr)?
49. How fast do humans grow (in km/hr)?
50. How many atoms are in the human body?
51. What is the spacing of these atoms?
52. Cannibalism is frowned on in most human societies. How many atoms of your great^n-grandfather who lived about 2000 years ago do you ingest with each meal?
53. If all the people of the world were crowded together, how much area would we cover?
54. Assuming one Santa Claus visits all Christian children on Christmas, how fast would he have to travel?
55. How many reindeer would he need to pull his sleigh?
56. What is the flow rate of the James River? Of the Mississippi River?
58. How many people were at the Million Man March in Washington DC? How would you estimate this?
59. How much carbon-dioxide does a square kilometer of forest remove from the atmosphere each year?
60. How much carbon-dioxide does an automobile add to the atmosphere each year?
61. How much carbon-dioxide does a human add to the atmosphere each year (by breathing)?
62. How many dump truck loads would it take to cart away Mt. Everest?
63. What is the mass of the Earth?
64. What are the relative sizes (radii) of the moon and the sun?

Transportation

65. What is the relative cost of fuel (per kilometer) of rickshaws and automobiles?
66. What is the relative waste generated (per kilometer) of rickshaws and automobiles?
67. What is the average cost of an automobile including overhead (maintenance, looking for parking, cleaning, etc)?
68. What is the average cost of a bicycle?
69. How much time would be saved nationwide by increasing the speed limit from 55 to 65 mph? How does this compare to the extra lives lost?
70. How far does a car travel before a one molecule layer of rubber is worn off the tires?

Mechanics

71. If comet Shoemaker-Levy had hit the Earth, how much energy would it have deposited? How does this compare to one year of solar radiation?
72. How long would it take a solar sail powered spaceship to travel to a) the Moon, b) Mars, c) Pluto?
73. How much work is done climbing a mountain (in kcal)?
74. How long would a beanstalk (elevator to geosynchronous orbit) have to be? What tensile strength would it require? How does this compare to steel, kevlar, spider silk, the maximum theoretical material strength?
75. What is the mass of the Earth?
76. What is the mass of the moon?
77. What is the rotational angular momentum of the Earth?
78. What is the rotational angular momentum of the Moon?
79. What is the maximum angular velocity the Earth could have without flying apart?
80. What is the tidal drag force on the Earth?
81. What is the revolutionary angular momentum of the Earth about the sun?
82. What is the revolutionary angular momentum of the Moon about the Earth?
83. What is Roche's limit (the orbital distance inside which a moon will disintegrate)?
84. How long was the day when the moon was at Roche's limit?
85. How long will the day be when it is equal to the month?
86. According to one hypothesis, 20% of the mass of the asteroid that killed the dinosaurs was uniformly deposited over the surface of the Earth at a density of 0.02 gm/cm^2. What was the mass of this asteroid?
87. What is the kinetic energy of a large (1 km^3) meteor? How does this compare to one year's insolation of the Earth? How much is this in megatons?
88. How much would a large (1 km^3) meteor strike change the angular momentum of the Earth?
89. How much energy is required to boil the Earth's oceans?
90. How often is the moon struck?
91. How large a collision is needed to split the moon in half? To split Phobos in half?
92. How small do you have to be to walk on water?
93. How high can mice and elephants jump?
94. How large a moon can you jump off of?
95. What is the kinetic energy of a drifting continent?
96. What is the height above the surrounding water of the Gulf Stream?
97. What is the depth below the surrounding water surface of the water surface over the Marianas Trench?
98. How much would the ocean surface rise if the ice caps melted? How much would that change the salinity of the ocean?
99. How much would the ocean surface rise due to global warming (in addition to ice cap melting)?
100. Astrology claims that the position of the planets at the time of our birth influences our lives. Calculate the relative gravitational attraction and the relative tidal forces on a newborn baby of a) Jupiter, b) the hospital building, c) the obstetrician.


Electricity and Magnetism

100. How strong are the magnets in the SSC? In the Fermilab ring?
101. How long would the Earth's magnetic field last without a dynamo?
102. What is the lifetime of a classical atom (before the electron loses 13 eV of energy to synchrotron radiation)?
103. What is the Schwarzchild radius of an electron?
104. At what distance is the magnetic field from high power transmission lines the same as a) the Earth's magnetic field? b) the magnetic field from your electric blanket?

Quantum Mechanics


105. What is the probability of an object suddenly jumping up from a surface?
106. How small can a 1 GB memory be?
107. What is the probability of a human diffracting as it walks through a doorway?
108. What is the probability of a human tunneling through a closed door?
109. You walk off of a cliff. How high does the cliff have to be (assuming constant g) for you to have an appreciable probability of quantum mechanically reflecting?


Energy


110. How long would a laser have to stay focused on a missile to ignite the chemical explosives in the warhead?
111. How much Uranium must the Earth contain to keep the core molten?
112. How long would the sun last without thermonuclear reactions?
113. What is the heat output of the sun?
114. If the Sun were made out of Gerbils, the Earth would be incinerated. Explain.
115. How much energy would be released by stellar collapse (i.e.: by the Sun shrinking from its present size down to a neutron star)?
116. How much waste (solid and gas) is created each year by a 1000-MWe coal power plant?
117. How much acid rain is caused each year by an unscrubbed 1000-MWe coal power plant?
118. How much waste (solid and gas) is created each year by a 1000-MWe oil power plant?
119. How much electrical power does the US use per year?
120. If 10% of Californians drive electric vehicles, how many extra power plants will it take to recharge them each night?
121. How much Iron, Glass, and Water does the US use per year?
122. How much waste does the US generate per year?
123. How much power do humans use? How does this compare to the solar energy incident on the Earth?
124. What is the heat output of a human?
125. What would be the resource value of a 1km^3 metallic asteroid?
126. How much power would it take to desalinate enough water for Virginia Beach?
127. How much flow is needed for a 1000 MegaWatt hydropower plant?
128. How much coal is needed each year for a 1000 MegaWatt coal fired power plant?
129. How much cooling water is needed for a 1000 MegaWatt nuclear or coal-fired power plant?
130. How much area would a 1000 Megawatt solar power generator need?
131. How much area would an orbital 1000 Megawatt solar power generator need?
132. How big would the earth-based receiving antenna be for an orbital 1000 MW solar power generator?
133. What would the power density be at the earth-based receiving antenna? Relative to the normal solar power density?


Nuclear Physics

134. How many neutrinos from the Surry nuclear power plant pass through you each year? How many interact? Is this harmful?
135. How much high-level nuclear waste is created each year by a 1000-MWe nuclear power plant?
136. If this waste was spread evenly over the surface of the earth, with what depth of soil would you have to mix it so that it would be safe to ingest (i.e.: within federal guidelines for ingestion of radioactivity)?
137. How long do you have to store the waste until it becomes reasonably safe?
138. What are the radiation levels a) in Norfolk, b) in Denver, c) in a commercial jetliner, d) near Three Mile Island at the time of the accident?
139. Ten neutrinos from Supernova 1987a (which was about 150,000 light years from earth) interacted and were detected in the Kamiokanda detector. If you were standing 2 AU from the supernova, what would have killed you?
140. What is a lower limit on the lifetime of the proton (based on the existence of life on earth)?
141. What is an upper limit on the energy released in cold fusion (based on the fact that it didn't kill its proponents)?
142. A biologist recently claimed to have revived a 30 million year old bacteria. How many cosmic rays would have passed through the bacteria during the last 30 million years? What is the probability that its DNA is scrambled?
143. How accurately can you date dinosaur bones?
144. Someone places 1 Curie of uranium on your chest. What do you die of?
145. How much is the energy content of 10 tons of 3He worth?
146. How much Uranium is needed each year for a 1000 MegaWatt nuclear plant?
147. How dangerous is Radon?
148. How dangerous was Three Mile Island?

Search for Extra Terrestrial Intelligence.


149. What is the dynamic range of the human eye?
150. What is the typical molecular binding energy?
151. What is the maximum size of various objects? Moons, planets, suns, white dwarfs, neutron stars, mammals, reptiles, bugs?
152. How likely is the existence of an extraterrestrial civilization?
153. What is the mean distance between civilizations?
154. How many extraterrestrial visits per year can we expect?
155. What is the probability of success for the Search for Extra-Terrestrial Intelligence?
156. What are the relative probabilities of dying (in the United States) of a) motor vehicle accident, b) gunshot, c) nuclear power plant accident and routine operation, d) coal power plant accident and routine operation, e) power line EM radiation, f) lightning strike, g) small meteor strike, h) large meteor strike, i) oil power plant accident and routine operation, j) plane crash?
157. What is the human power output in the radio spectrum relative to the Earth's blackbody radio radiation? 158. Relative to the Sun's radio emission (black-body)?
159. A balloon full of freon falls to the floor. How much freon do you expect to find in the upper atmosphere?

These problems were written and collected by L.B. Weinstein with help from John Adam, Charles Hyde-Wright, and Marc Sher. These problems may be freely used in classrooms. They may be copied and cited in published work if L.B. Weinstein is acknowledged and this URL is given:

L.B. Weinstein, Old Dominion University.

More from London District Science Olympics

160. How many grains of sand are there on all the beaches surrounding Lake Erie?.
161. How many bricks are there in London?
162. How many electrons do you have in your body?
163. How many snowflakes fall on U.W.O. if the total accumulation is 10 em? (number of snowflakes).
164. What is the mass of all the automobiles scrapped in North America this month? (kilograms).
165. How many molecules of ink were used in the daily newspapers of Canada today? (number of molecules).
166. How much has the mass of the human population increased in the last year? (kilograms).
167. How many air molecules in an automobile tire? (a number).
168. It is Hockey Night in Canada, and Londoners sit down to watch the game. How much water has to go over Niagara Falls to power their television sets during, the game? (litres).
:169. How many photons/sec are emitted by a 100 watt light bulb? (number of photons)
170. If the mass of one million molecules of water could be converted entirely into energy in the form of heat, what volume of water, initially at room temperature, could it bring to a boil? (litres)
171. What is the weight of the air over Lake Superior? (Newton's)
172. How much work is done in dragging a suitcase of clothes from Vancouver to Halifax? (joules)
173. How much power per square metre is carried by the wind on a breezy day? (watts)
174. How much does the Thames river heat up in going over the Fanshawe Dam? (degrees Celcius)
175. How much energy does a horse consume in its lifetime. (joules)
176. What force is required to break a blade of grass by pulling at each end? (newtons )
177. How many joules are there in on(.- litre of gasoline?
178. The marathon runner starts off at the same time as the radar signal leaves the earth for ,Jupiter. He stops when the echo is received back on earth. How far does he run? (kilometres)
179. The Space Shuttle is in an orbit which takes it over London and then Kitchener. How long does it take to get from London to Kitchener? (seconds)
180. How big does a seed on the ground have to be to justify a bird in flying off a tree branch to eat it? (kilograms)
181. How many cars per hour can leave London on highway 401? (number of cars)
182. What is the maximum force required to hold a .25 calibre pistol steady while firing it? (newtons)
183. How many uranium atoms must undergo fission to supply electricity to an average household for one day? (number of uranium atoms)
184. How many people are employed delivering mail in Vancouver? (number of people)
185. What is the force exerted on a large tree by gale winds? (newtons)
186. What would the air in this room weigh on Mars? (newtons)
187. How many atoms are there in the period at the end of this sentence? (number of atoms).
188. Suppose the electrons that strike the surface of the picture tube in your television set were actually able to travel unimpeded to the moon. How long would they take to get there? (seconds)
189. If you breath on a window in the winter. a patch of mist will form (1i) the glass. What is the mass of that patch? (kilograms)
190. If all the water in the world's oceans were put in a sphere, what would its radius be? (metre")
191. a person runs up to the top of the CN tower. How many ice cubes could be melted by the expenditure of the same amount: of energy? (number of of cubes)
192. Consider the possibility of a large country such as China organizing a "geophysical weapon", by having all the inhabitants of China jump off` chairs onto the ground at the same instant. Assuming; that the resulting; energy could all be focussed to one point on the earth, how many kilograms of TNT would this weapon correspond to? (kilograms of TNT)
193. How much energy is required to get the Space Shuttle into orbit? (joules)
194. What is the thickness of this paper in wavelengths of visible light? (number of wavelengths)
195. If it were actually possible for an ant to walk to the Andromeda galaxy, how long would it take it to complete the trip? (years)
196. Sometimes there is a certain attraction between a man and a woman when they meet, but there is always a gravitational attraction between then: Estimate the magnitude of that gravitational attraction as they stand talking to each other.(newtons)
197. A helium-filled balloon is 50 cm. in diameter. What is its diameter when taken to the bottom of the Atlantic ocean? (metres)
198. People crowd into London until all available open space within the city limits is covered with standing people. How many people would there be? (a number)
199. It is a clear day, and the sun is shining almost straight down on the backyard swimming pool. How much will the water temperature change in 5 minutes? (^o C).
200. In the North-West Territories the mosquitoes can be so numerous that a person standing in the muskeg is completely covered by the insects. How many insects would that require? (number of mosquitoes)
201. What is the total mass of the trees in the "Forest City"? (kilograms)
202. How many earthworms will inhabit a 100 hectare pasture field? (number of earthworms)
203. Estimate the mass of lead deposited per square metre per year in London due to airborne lead emitted from cars, given that each litre of gasoline contains about 2 grams of lead. (kilograms)
204. How much kinetic energy is converted into heat by water striking the ground on a normal city block during a typical thunderstorm? (joules)
205. How many words are there in the books in the main branch of the London Public Library? (number of words)
206. If a golf ball were the size of Jupiter, how deep would the dimples be? (metres)
207. How many red blood cells are there in Michael Jackson'? (number of red blood cells)
208. You want to have a cup of tea with your peanut, butter and jam sandwich. You consume part of the sandwich in a special device which uses the chemical energy in the sandwich to boil the water for your tea. If this device is 100% efficient, what fraction of the sandwich is required to make your tea? (fraction of a sandwich)
209. Determine the number of oxygen molecules that pass in and out of the lungs of' an adult human in one day. (number of oxygen molecules)
210. What is the mass of the great pyramid of Cheops? (kilograms)
211. Calculate the number of C02 molecules that are produced from the complete combustion of one litre of gasoline. (number of C02 molecules)
212 . How many kittens were born in the city of London last year? (number of kittens)
213. Compute the energy collecting surface area of all the leaves of a full grown maple tree. (square metres)
214. A space traveller on Mars observes the earth's moon. What angle will it subtend when it is closest to Mars? (degrees)
215. Estimate the number of layers of molecules of rubber lost by a tire on a car each time it revolves while driving. (number of molecular layers)
216. Some people are able to inscribe as many as 100 words on the head of a pin e.g. the Lord's Prayer How many atoms: are displaced by the letters?
217. How many molecules strike your nose each second? (number of molecules)
218. How many 4 litre cans of yellow paint would be needed to paint a lane divider on the 401 between London and Toronto? (number of cans)
219. Estimate the number of ethanol molecules in a bottle of Labatt's Blue. (number of ethanol molecules)
220. How many grains of salt in an average salt shaker? (number of grains)
221. Protons and antiprotons can completely annihilate each other, and produce energy in the form of gamma rays. If this energy could be all converted into electricity, at what rate would the particles need to be annihilated to light a 100 watt light-bulb? (annihilations per second)
222. How long does it take for the electrons in a TV tube to get from the electron gun to the screen? (seconds)
223. If all the atoms in an elephant were put into a line, how long would that line of atoms be? (metre)
224. Estimate how many kilograms of potatoes are eaten each year in North America. (kilograms)
225 1 wire 10 cm long and 1 mm in diameter carries a current of 1 A. How long does it take the individual electrons to get from one end of the wire to to the other using a DC source? (seconds)
226 1 wire 10 cm long and 1 mm in diameter carries a current of 1 A. How long does it take the individual electrons to get from one end of the wire to to the other using an AC source? (seconds)
227 What is the total kinetic energy of all the automobiles in Canada at this moment? (joules)
228. What force does the earth exert on Jupiter when they are closest.? (newtons)
229. How long would it take an amoeba to travel around the circumference of the earth, supposing that it moved in a straight line at top speed, and could live that long? (seconds)
230. If there were a mole of butterflies lying evenly distributed ever the earth, how thick a layer would they produce? (metres)
231. When the island of Krakatoa was destroyed by a volcanic eruption, the low pressure sound waves could be detected world-wide. How long would it take for such a wave to travel around the earth and come back to Krakatoa? (seconds)
232. What is the area of Ontario? (square metres)
233. How many cells are there in an apple? (number of cells)
234. A 10 year old car is badly rusted. If it rusted at a uniform rate, estimate how many iron atoms each day combine with oxygen to form rust? (number of iron atoms)
235. How many individual hairs does a barber cut. in a lifetime? (number of hairs)
236. How many traffic lights are there in Toronto? (number of traffic lights)
237. How many Si02 molecules in a grain of sand? (number of Si02 molecules)
238. How many atoms do you have in your lungs that were also in the last breath of Julius Caesar? (number of atoms)
239. What is the mass of the CN tower? (kilograms
240. How many photons of visible light are emitted in a single flash of a camera flash gun? (number of photons)
241. If you were to bore a hole straight the earth from London, Ontario, you would come out how far from London, England? (kilometres)
242. What is the mass of all the tennis racquets in the world? (kilograms)
243. How many molecules in an average human body? (number of' molecules)
244. How many swimming strokes to swim from Grand Bend to Goderich? (number of s strokes )
245. How many dimples are there on a basketball? (number of' dimples)
246. How many ethanol molecules in a bottle of good Scotch? (number of molecules)
247. How much energy can justifiably be expended to persuade one high school student to take Physics? (joules)
248. How much warmer is a room when there are ten people in it than when it is empty? (degrees C)
249. What is the total daily energy requirement of' the city of London? (,joules)
250, how many worms does a rob:in eat in a dory? (number of worms)
251. How much do the brakes of a passenger car- heat up in stopping at. a stop sign? (degrees C)
252. How wide a creek can a man jump with a running start? (metres)
253. How far-can a person throw a stone? (metres)
254. What is the mass of all of the world's fingernail clippings from today'? (kilograms)
255. How far away could you hear the music, if a 30 watt stereo could put all of its output power into sound? (kilometres)
256. What is the speed of Titan in its orbit around Saturn? (metres/sec)
257. How many hairs are there on a dog?
258. How many molecules will evaporate each minute from a saucepan of water left to stand in the shade on a dry summer's day? (number of molecules)
259. If the conversion of electrical energy to light energy is 75% efficient, how many photons are emitted per second by a 40 watt fluorescent tube? (number of photons/sec)
260. How fast must a hummingbird beat its wings in order to hover a t 4 m above the ground (number of beats/sec)
261. How long would it take a signal to make a round trip to the sun through inverters (IC's)? (seconds)
262. On the beach at noon, with a clear sky, you made a good snapshot at f/8, and 1/500 sec/ At midnight the same scene is lit by the full moon. You want to make an equally well-exposed picture. You have a tripod to hold the camera for a time exposure, and the aperture can be opened up to f/2.8. What would be a good exposure time to try? (seconds)
263. Near the top of the atmosphere an energetic cosmic ray proton strikes a nucleus. A fast neutron emerges from the explosion, travelling straight downwards. What is the probability that it will reach the earth's surface without having passed through a nucleus lolls? (probability)
264. Estimate the total Canadian annual energy requirement. (kilograms)
265. What is the probabilty of winning a million dollars on Who Wants to ba a Millionaire by guessing? Assume everyone guesses, including the audience and teh phone-a-friend.
266. What is the chance from pure guessing that a team will take home the top prize on Greed?
267.How many eggs are consumed in an average week in the United States?
268. How many dozens of eggs are consumed in the United States during the week that contains Easter?
269. How many electrons are there on the earth?
270. According to the Canadain Blood Service, how many litres of blood are donated in Canada in the average year? (Hint: One unit of blood is equal to about 450 mililitres).
271. How many compact discs were shipped to record stores in the United State in 1999?
272. How many runs were scored by major league baseball teams during April 200?
273. On average, how much energy is released when one litre of gasoline is burned?
274. Including the fjords, what is the length of the coastline of Norway?





Judging 1. The papers will be marked using the scheme described above.
2. The team with the highest score wins.
Enrico Fermi

Enrico Fermi

Enrico Fermi, 1901-1954, won the Nobel Prize in 1938 for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons. He led the group that produced the first nuclear reactor, in Chicago in 1942. We remember him in the Science Olympics for his skill in estimating quantities when very little information is available. He once estimated the energy released in an atomic explosion by dropping little pieces of paper, and seeing where they landed down wind.

He amused his friends by inventing questions which have a whimsical quality about them; one of the most famous is "How many Piano Tuners are there in New York City?" A very readable non-scientific account of his life is given in the delightful book "Atoms in the Family", written by his wife, Laura Fermi.

A "Fermi question" is thus a question which seeks a fast, rough estimate of a quantity which is either difficult or impossible to measure directly. For example, the question "How many drops of water are there in Lake Erie?" requires an estimate of the volume of a drop, the volume of Lake Erie from approximate dimensions and conversion of units to yield an answer. This answer would be an estimate hopefully accurate within a factor of ten.


EDUCATIONAL RATIONALE

Source: http://aries.phys.yorku.ca/~rothery/fermi/fermi.edu.html

No one likes to hear stories of "doom and gloom" these days. But the current level of science literacy in North America can only be described as "woeful." The long-term consequences of a largely scientifically illiterate population are very serious and ultimately debilitating to any modern society.

Rather than complain interminably, some educators such as Richard Light offer thoughtful advice about how best to remedy this state of affairs, regardless of who's to blame. Ranking very high on the list for improving critical thinking skills and scientific common sense at all levels is, Fermi Questions.

Fermi Questions build problem-solving skills and develop much-need estimation skills. It is critically important that a successful student have a "feel" for whether an answer is reasonable or not. The beauty of a Fermi Question is that the methodology, that is, the formulation of a solution, is more important than the answer itself: Indeed there is no "correct" answer to a Fermi Question, only a range of answers. Moreover, memorization of facts becomes much less important than developing the logical tools necessary to solve such questions. The sooner students are introduced to this way of thinking in science, particularly the physical sciences, the better. From a student's perspective, the "coolest" thing about Fermi Questions is that they're fun, or at least can be made so relatively easily. What more can one ask?

Finally, just what is a Fermi Question? Philip Morrison, in a Letter to the Editor of the American Journal of Physics in 1963, said it best in the following excerpt in which he is commenting on the training of undergraduate physics majors. But it should be noted that Fermi Questions are appropriate for all levels of education, including elementary and secondary schools.

"It is by no means possible to specify the training and readiness of a prospective graduate student by a mere list of topics. There is a kind of power over the theoretical and experimental studies in which he has engaged which is difficult to define, but whose presence is perhaps more important than much knowledge which is more formal and complete. There is one test for such power which is at the same time a remarkably apt method for its development. That is the estimation of rough but quantitative answers to unexpected questions about many aspects of the natural world. The method was the common and frequently amusing practice of Enrico Fermi, perhaps the most widely creative physicist of our times. Fermi delighted to think up and at once discuss and to answer questions which drew upon deep understanding of the world, upon everyday experience, and upon the ability to make rough approximations, inspired guesses, and statistical estimates from very little data.

Such questions can of course be found for nearly any level of education. [The] conception of experiments and the formation of theoretical hypotheses are activities which are well simulated by asking and answering good Fermi questions."


Source Enrico Fermi

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