A neutral pion initially at rest decays into two gamma rays: π^0 →γ+γ. Calculate the wavelength

step 1 A neutral pion initially at rest decays into two gamma rays. Calculate the wavelength of the gam

A neutral pion initially at rest decays into two gamma rays:...

Key Concepts

Two-body Decay Kinematics

In a two-body decay where the initial particle is at rest, the decay products move in exactly opposite directions with equal magnitudes of momentum. This symmetric configuration simplifies the analysis since both particles share equal amounts of kinetic energy, which is crucial for understanding why they exhibit identical wavelengths when they are photons.

Photon Energy-Wavelength Relationship

The energy of a photon is related to its wavelength by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. This formula is essential for converting the energy calculated from conservation principles into a wavelength, allowing direct determination of the observed photon wavelength.

Conservation of Energy

In any particle interaction, including decays, the total energy before and after the event must remain constant. In the context of a decay process, the energy from the rest mass of the original particle is converted into the energy of the decay products. This is crucial for determining the energy—and thus the wavelength—of the emitted photons.

Conservation of Momentum

The law of conservation of momentum states that the total momentum of an isolated system remains constant. When the decaying particle is initially at rest, the momentum carried away by the decay products must sum to zero, meaning that produced photons must have equal and opposite momenta. This directly implies that their energies are equal, assuming they are massless and move at the same speed, leading to the same wavelength.

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