Assume a photomultiplier tube (Fig. 40.12) has seven dynodes...

Assume a photomultiplier tube (Fig. 40.12$)$ has seven dynodes with potentials of $100,200,300, \ldots, 700 \mathrm{V}$ . The average energy required to free an electron from the dynode surface is 10.0 eV. Assume only one electron is incident and the tube functions with 100$\%$ efficiency. (a) How many electrons are freed at the first dynode? (b) How many electrons are collected at the last dynode? (c) What is the energy available to the counter for each electron?

Key Concepts

Photomultiplier Tube Operation

Photomultiplier tubes are devices used to detect and amplify weak light signals. They work by converting incident photons into electrons via a photocathode, then amplifying the resulting electron signal through a series of dynodes where secondary electron emission takes place, leading to a measurable current.

Secondary Electron Emission

Secondary electron emission is the process in which a single electron, striking a material with sufficient energy, causes the release of multiple electrons from that material. This phenomenon is fundamental in devices like photomultiplier tubes where the initial electron is amplified as it cascades through successive stages.

Electrostatic Energy Conversion

Electrostatic energy conversion involves transforming the electrical potential difference experienced by a charged particle, such as an electron, into kinetic energy. The energy gained by the electron as it moves across a voltage difference is given by the product of its charge and the voltage (E = qV), which is exploited in the amplification stages of photomultiplier tubes.

Electron Multiplication Gain

Electron multiplication gain refers to the overall increase in the number of electrons as they are multiplied through successive stages of secondary emission. The multiplication factor is determined by the efficiency and the number of stages (dynodes), culminating in a large number of electrons collected at the final stage relative to the initial electron generated by the photocathode.

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