What is the half-life of a pion in the reference frame of...

What is the half-life of a pion in the reference frame of the patient undergoing pion therapy?
A. $1.8 \times 10^{-10} \mathrm{s}$
B. $1.8 \times 10^{-8} \mathrm{s}$
C. $1.8 \times 10^{-7} \mathrm{s}$
D. $1.8 \times 10^{-6} \mathrm{s}$

Key Concepts

Pions

Pions are subatomic mesons that play a key role in mediating the strong force in nuclear physics. They are unstable particles with characteristic lifetimes and decay channels, and understanding their decay properties is important for both theoretical studies in particle physics and practical applications such as certain types of particle therapy.

Reference Frames

A reference frame is a coordinate system or perspective from which physical measurements are made. In contexts involving high-speed particles, choosing the proper frame—such as the rest frame of the particle—ensures that intrinsic properties like lifetime are measured without relativistic effects, such as time dilation.

Proper Lifetime

The proper lifetime of a particle refers to the time interval measured in the particle’s own rest frame before it decays. This measurement is intrinsic to the particle and serves as a baseline from which decay behavior in other reference frames, affected by time dilation, can be computed.

Exponential Decay

Exponential decay describes the process by which the number of particles decreases at a rate proportional to the current number, leading to a situation where after one half-life, about half of the original quantity has decayed. This concept is fundamental in understanding how unstable particles and radioactive materials decay over time.

Half-Life

Half-life is a measure of the time required for a given quantity of an unstable entity, such as a radioactive particle or a subatomic particle, to decrease by half through exponential decay. It is a characteristic constant that helps describe the decay process and is independent of the starting amount.

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