In a Geiger tube, the voltage between the electrodes is typically 1.00 kV and the current pulse

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In a Geiger tube, the voltage between the electrodes is...

In a Geiger tube, the voltage between the electrodes is typically 1.00 $\mathrm{kV}$ and the current pulse discharges a $5.00-\mathrm{pF}$ capacitor. (a) What is the energy amplification of this device for a 0.500 -MeV electron? (b) How many electrons participate in the avalanche caused by the single initial electron?

Key Concepts

Capacitor Energy Storage

A capacitor stores electrical energy determined by its capacitance and the voltage across it, following the formula E = 1/2 C V². In contexts such as radiation detectors like a Geiger tube, the sudden discharge of this stored energy in response to an ionizing event is central to converting the physical event into a measurable electrical signal.

Gas Ionization and Avalanche Process

In gas-filled detectors, an initial ionizing event (such as a charged particle entering the tube) produces a free electron which, under a strong electric field, accelerates and collides with gas molecules. This collision causes further ionization, resulting in an exponential multiplication of free electrons—a phenomenon known as the ionization avalanche, which is key to signal amplification in the detector.

Energy Amplification Factor

The energy amplification factor in radiation detection is the ratio of the total energy released (or measured) during the detector's discharge to the initial energy deposited by the incoming particle. This concept is crucial for understanding how a small energy input can lead to a much larger output signal, thereby enabling the detection of individual ionizing events.

Radiation Detection Principles

Radiation detection in devices like Geiger tubes relies on converting the energy from ionizing particles into an electrical signal. The underlying principles involve the initial ionization caused by the particle, the subsequent avalanche multiplication of charge carriers, and the eventual discharge of stored energy in a capacitor, all of which work together to produce a detectable pulse corresponding to the original event.

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