A laboratory calibration source contains sodium-22

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

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

Problem

A laboratory calibration source contains sodium-22, which decays by positron emission. Nearly every decay leaves the neon-22 nucleus in an excited state; take the rare branch that goes directly to its ground state:

^{22}\mathrm{Na} \to {}^{22}\mathrm{Ne} + e^+ + \nu

The masses of the neutral atoms are

M(^{22}\mathrm{Na}) = 21.994437\ \mathrm{u}

and

M(^{22}\mathrm{Ne}) = 21.991385\ \mathrm{u}

, with

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

and

m_ec^2 = 0.511\ \mathrm{MeV}

. The neutrino mass is negligible and electron binding energies in the atoms are ignored throughout. Each emitted positron slows down in the surrounding material and annihilates with an electron of that material when both are effectively at rest in the laboratory frame

S

, producing two photons. ((a)) Find the

Q

value of the decay, that is the energy shared by the neon nucleus, the positron and the neutrino. ((b)) Find the energy of each annihilation photon in

S

. ((c)) Find the total energy released per decay once the positron has annihilated (counting the neutrino's share).

Related theory

Nuclear Physics

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