A hospital pharmacy must prepare a dose of the medical isotope whose half–life is

PHYSICS · Multi-part · CBSE · Physics · Nuclei · Nuclei

Problem

A hospital pharmacy must prepare a dose of the medical isotope

^{99\mathrm{m}}\!\mathrm{Tc}

whose half–life is

6.0\,\text{h}

. The required activity at the instant the syringe will be handed to the physician is

15\,\text{GBq}

. (Molar mass of technetium

=99\,\text{g mol}^{-1}

; Avogadro number

N_A = 6.02\times10^{23}\,\text{mol}^{-1}

.) (i) Calculate the decay constant of

^{99\mathrm{m}}\!\mathrm{Tc}

. (ii) Determine the number of radioactive nuclei that must be present in the syringe at that instant. (iii) Hence find the mass of

^{99\mathrm{m}}\!\mathrm{Tc}

that must be delivered to the hospital.