A least-squares fit to Kurie-plot data for an allowed emitter

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Nuclear Physics · Radioactivity and decay modes

The Nucleus Resolved, Ch Beta decay: Fermi's theory, parity violation and the double beta modes

Problem

A least-squares fit to Kurie-plot data for an allowed β−\beta^- emitter, taken over the range Te=0.1T_e = 0.1 to 0.5 MeV0.5\,\mathrm{MeV}, gives the straight line K(Te)=45.2−62.5 (Te/MeV)K(T_e) = 45.2 - 62.5\,(T_e/\mathrm{MeV}) with KK dimensionless and TeT_e in MeV. ((a)) Using K(Te)=C(Q−Te)K(T_e) = C(Q - T_e), find the endpoint energy QQ. ((b)) The closest data point used in the fit is at Te=0.5 MeVT_e = 0.5\,\mathrm{MeV}. State the energy gap, in eV, between this point and the endpoint found in part (a), and explain why this measurement could not detect or exclude a neutrino mass of order 1 eV1\,\mathrm{eV}.

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