Carbon-11 decays by positron emission to the ground state of boron-11: ^ 11 C ^ 11 B…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime

Relativity and Gravitation, Ch Mass as energy: binding, defect and annihilation

Problem

Carbon-11 decays by positron emission to the ground state of boron-11:

^{11}\mathrm{C} \to {}^{11}\mathrm{B} + e^+ + \nu

Neutral-atom masses are

M(^{11}\mathrm{C}) = 11.011434\ \mathrm{u}

and

M(^{11}\mathrm{B}) = 11.009305\ \mathrm{u}

;

1\ \mathrm{u} = 931.494\ \mathrm{MeV}/c^2

m_ec^2 = 0.511\ \mathrm{MeV}

. The neutrino mass and the electron binding energies in the atoms are neglected. In a thin gas target one such positron, still in flight with kinetic energy

K = 0.900\ \mathrm{MeV}

in the laboratory frame

S

, annihilates with an electron at rest in

S

. Two photons are produced, and in this event both travel along the positron's original line of flight, one forwards and one backwards. ((a)) Find the

Q

value of the decay. ((b)) Find the invariant mass energy

M_{\rm inv}c^2

of the electron-positron system just before the annihilation. ((c)) Find the energy of the forward photon and of the backward photon in

S

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