Problem — Fermi estimate, school experiments in Italy

Problem

Estimate the number of physics experiments carried out every year in all Italian upper secondary schools (licei). State the factors (number of licei, upper-cycle classes with a lab, experiments per class) and keep track of the orders of magnitude.

Solution

A Fermi estimate proceeds by breaking down the sought quantity into factors, each estimated by order of magnitude, and then multiplying the orders of magnitude.

Factor 1 — number of licei. In Italy the licei (in particular the scientific ones, where the physics lab is most widespread) are of the order of a thousand: $N_\text{licei} \sim 10^3$

Factor 2 — upper-cycle classes with a lab. In each liceo the upper-cycle classes that carry out lab activities are a few per year of study, hence of the order of $\sim 10$ classes per liceo. The total number of classes is $N_\text{classi} \sim 10^3 \times 10 = 10^4$

Factor 3 — experiments per class per year. Each class carries out of the order of $\sim 10$ experiments in a school year.

Product of the orders of magnitude. $N_\text{esp} \sim N_\text{classi} \times 10 = 10^4 \times 10 = 10^5$

The result does not claim exactness: it gives the correct order of magnitude, roughly one hundred thousand experiments per year.

$\ev{N_\text{esp} \sim 10^5 \ \text{experiments/year}}$

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Topics: Metodo sperimentale Skills: Stime di Fermi