Typical measurements of the mass of a subatomic delta particle (m ≈1230 MeV / c^2) are shown in

step 1 of this given question so and we can clearly see that the mass mass is approximately equals to 1

Typical measurements of the mass of a subatomic delta...

Typical measurements of the mass of a subatomic delta particle $\left(m \approx 1230 \mathrm{MeV} / c^{2}\right)$ are shown in Figure $\mathrm{P} 5.26$ Although the lifetime of the delta is much too short to measure directly, it can be calculated from the energy-time uncertainty principle. Estimate the lifetime from the full width at half-maximum of the mass measurement distribution shown. Figure P5.26 Histogram of mass measurements of the delta particle.

Typical measurements of the mass of a subatomic delta particle $\left(m \approx 1230 \mathrm{MeV} / c^{2}\right)$ are shown in Figure $\mathrm{P} 5.26$ Although the lifetime of the delta is much too short to measure directly, it can be calculated from the energy-time uncertainty principle. Estimate the lifetime from the full width at half-maximum of the mass measurement distribution shown.
Figure P5.26 Histogram of mass measurements of the delta particle.

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Key Concepts

Energy-Time Uncertainty Principle

This principle states that there is a fundamental limit to the precision with which energy and time can be simultaneously known. In quantum mechanics, it provides a relation between the uncertainty in energy measurements (such as the width of a resonance) and the lifetime of a state, implying that a short-lived particle must have a broad energy (or mass) distribution.

Decay Width and Lifetime Relationship

In the study of unstable particles, the decay width—often characterized by the full width at half-maximum (FWHM) of the mass distribution—is inversely related to the particle's lifetime. Essentially, a larger decay width corresponds to a shorter lifetime. This quantitative relation is derived from the energy-time uncertainty principle, allowing physicists to estimate lifetimes from measured mass distributions.

Resonance in Particle Physics

Resonance refers to a temporary state or an unstable particle that is produced in high-energy collisions. These states, such as certain baryons or mesons, decay very quickly, leading to a spread in the measured mass. The resonance phenomenon and its associated mass distribution are key in identifying and studying these fleeting particles, providing insights into their properties and interactions.

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