Abstract:

An innovative extracurricular educational path was experimented in two classes of Secondary School students. The activity concluded a joint project for scientific literacy in which the class teachers of mathematics and physics had been involved. During the first part of this project the teachers introduced the concept of photon – a massless particle if taken on its own – and deduced mass-energy equivalence in variation form through the adaptation of an Einstein’s thought experiment (1905) on the decrease of mass of a body emitting electromagnetic radiation, showing that the emitted energy ΔE causes a variation of mass given by Δm = ΔE/c^2.

Our path began with a brief historical introduction to radioactivity (for example describing the notorious experiment by Pierre Curie with electroscope) and to α, β, γ decays. Then we defined mass operationally at atomic-nuclear level through the measure performed by a mass spectrometer. Two nuclide maps were shown to students, coloured according to the mean life and the “mass excess” (defined as Mnucleus – ∑ Mnucleons) respectively. Students performed a hands-on calculus of the atomic mass variation when passing from the corresponding nuclide to the daughter in a α or β decay afterwards. The aim of this part was to make students conscious that mass is not conserved in nuclear processes, in order to generate a discourse between different models on mass in them.

After that, we illustrated a thought experiment on a photon rebounding against the walls of a uniformly accelerated box, correlating the effects of the interaction photon-box to the inertial characteristic of the whole system.

We modelled the matter-radiation interaction in the box as a Compton inelastic collision between a photon and an external electron of box wall atoms and we represented the cause of the fixed acceleration with an external force Fext: starting from total energy and linear momentum conservation and exploiting the De Broglie equation, at the first order of approximation we obtained the following expression for the external driving force: Fext = (M + E/c^2)a , where E is the initial photon energy, M the box mass, a the box acceleration. This expression brings to the interpretation that the system composed by the photon and the box acts as if its «effective» mass were M + E/c^2.

Keywords:

Photon, thought experiment, radioactive decay, mass, mass-energy equivalence.