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Fermi Questions – Activity Directions


Enrico Fermi

Enrico Fermi (1901-1954) was an Italian physicist who made significant discoveries in nuclear physics and quantum mechanics. In 1938, he received the Nobel Prize in physics for his discovery of nuclear reactions caused by slow neutrons. This mechanism led directly to the development of atomic bombs and nuclear fission reactors. After receiving his Nobel Prize, he emigrated with his family to the United States to escape the fascist regime of Benito Mussolini, where he soon began contributing to the Manhattan Project.

Fermi was famous for being able to make good estimates in situations where very little information was known. When the first nuclear bomb was tested, Fermi was nearby to observe. To get a preliminary estimate of the amount of energy released, he sprinkled small pieces of paper in the air and observed what happened when the shock wave reached them. (Being so close to the bomb on this and many other occasions exposed Fermi to dangerous radiation that led to his death by stomach cancer at the age of 53. Fermi was aware of the danger, but chose to work on this project anyway because he believed that the work was vital in the fight against Fascism.) Fermi often amused his friends and students by inventing and solving whimsical questions such as "How many piano tuners are there in Chicago?".

A "Fermi Question" asks for a quick estimate of a quantity that seems difficult or impossible to determine precisely. Fermi's approach to such questions was to use common sense and rough estimates of quantities to piece together a ball-park value.

For example, one way to estimate the number of piano tuners in Chicago is to break the process into steps: estimate the population; estimate the number of households in the population; estimate the fraction of households that have pianos; estimate how often each household has its piano tuned; estimate the time it takes to tune a piano; estimate how many hours a piano tuner would work each week.

In this case, it is possible to check the estimate by looking in the phone book to see how many piano tuners are actually in Chicago.

Fermi Questions in Everyday Life

Here are a few examples of practical Fermi Questions.

It is empowering to cultivate your ability to think about these kinds of big picture questions. Thinking this way can enable you to dream big and accomplish your goals. Practicing this skill can equip you to identify opportunities and dangers that are not apparent to most people.

Fermi Questions Lab

Record your answers to each question on another page. Be sure to write your team name, list the members of your team, and write out the Fermi question you are investigating.

  1. Question: State the question and discuss how you will interpret it.
  2. Wild Guess: What is your answer without any calculating?
  3. Educated Guess: List the pieces of information you will need to answer this Fermi question more precisely. Estimate the value of each quantity in your list. Based on your estimates, what is your solution to the Fermi question? Show all your steps and use words to explain them.
  4. Variables and Formulas: Choose variable names for each quantity that you estimated. Write a series of formulas or a procedure that explains how you used the quantities to find the solution. Try to simplify the process into a single formula that answers the Fermi question if possible.
  5. Gathering Data: Perform experiments, conduct surveys, make measurements, or search for information that would help you to obtain a more precise estimate. For each quantity, identify the smallest possible value, the largest possible value, and the most likely value (you will have to use your best judgment to estimate these values). Then use the formula you found in the previous step to find the smallest likely answer to the Fermi question, the largest likely answer to the Fermi question, and the most likely answer to the Fermi question. Show your work!
  6. Conclusions: State your final answers to the question. Explain some possible sources of error in your procedure. List any interesting facts that you learned while seeking the answer to the Fermi question. Finally, describe a further direction that you could pursue if you wanted to extend your investigation into this topic.

Sample Fermi Questions

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