The neutral pion (π^0) is an unstable particle produced in...

The neutral pion $\left(\pi^{0}\right)$ is an unstable particle produced in high-energy particle collisions. Its mass is about 264 times that of the electron, and it exists for an average lifetime of $8.4 \times 10^{-17} \mathrm{s}$ before decaying into two gamma-ray photons. Using the relationship $E=m c^{2}$ between rest mass and energy, find the uncertainty in the mass of the particle and express it as a fraction of the mass.

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Key Concepts

Mass-Energy Equivalence

This principle, encapsulated by the equation E=mc², indicates that mass can be converted into energy and vice versa, establishing a fundamental link between the two. It allows physicists to relate the rest mass of a particle to its energy content, which is essential for understanding processes like particle decay.

Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle posits that certain pairs of physical quantities, such as energy and time, cannot be simultaneously measured with arbitrary precision. In the context of particle decay, the finite lifetime of a particle leads to an inherent uncertainty in its energy, which, via mass-energy equivalence, translates into an uncertainty in its mass.

Lifetime and Energy Uncertainty in Particle Decay

For unstable particles, the short lifetime introduces a measurable uncertainty in the energy state of the particle. This energy uncertainty, when related back to mass using the E=mc² relationship, results in a corresponding uncertainty in the mass measurement. The shorter the lifetime of the particle, the greater the uncertainty, reflecting the quantum nature of particle decay.

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