A photon of energy travels along the axis of the laboratory frame and strikes a free…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Particle Physics & Quantum Fields · Particles, interactions and experiment

Relativity and Gravitation, Ch Relativistic momentum, energy and collisions

Problem

A photon of energy

E_{\rm in} = 300.0\ \mathrm{keV}

travels along the

+x

axis of the laboratory frame and strikes a free electron at rest there. The electron has mass

m_e = 511.0\ \mathrm{keV}/c^2

. After the collision the photon travels at

\theta = 60.0^\circ

to the

+x

axis, in the

xy

plane; the electron recoils in the same plane. The system is isolated, so four-momentum is conserved, and for a photon

E = pc

. ((a)) Using conservation of four-momentum, show that

E_{\rm out} = E_{\rm in}\big/\left[1 + (E_{\rm in}/m_ec^2)(1-\cos\theta)\right]

and evaluate

E_{\rm out}

in keV. ((b)) Find the kinetic energy of the recoiling electron, in keV. ((c)) Find the angle between the recoiling electron's momentum and the

+x

axis, in degrees.

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