An industrial gauging device uses a sealed γ-emitting source containing N0=3.0×1012 undecayed nuclei. The half-life of the nuclide is 45d and each decay emits a γ-ray of energy 1.5MeV.
(a) Derive an expression for the total energy emitted (in joule) by the source between day 20 and day 60 after installation.
(b) Calculate the numerical value of this energy.
(c) A worker is allowed to receive at most 5.0×10−4J of γ energy from this source during that period. Assess, with calculation, whether the device can operate safely for the worker between day 20 and day 60.