Step 1: Understanding the Question:
The question asks for the half-life of Caesium-137 ($^{137}Cs$), which is one of the two primary isotopes used in industrial food irradiation facilities.
Step 2: Detailed Explanation:
• Food Irradiation Isotopes: To irradiate food, gamma rays are typically sourced from either Cobalt-60 ($^{60}Co$) or Caesium-137 ($^{137}Cs$).
• Half-Life Concept: The half-life is the time required for half of the radioactive nuclei in a sample to decay. It determines how often the source needs to be replenished.
• $^{137Cs$ Data:} Caesium-137 has a half-life of approximately $17$ years. In multiple-choice questions, this is commonly rounded to $30$ years.
• Comparison with $^{60Co$:} Cobalt-60 is much more common in industry but has a much shorter half-life of approximately $5.27$ years.
• Decay Process: $^{137}Cs$ decays into Barium-137m, which then emits a $0.662$ MeV gamma ray used for processing.
Step 3: Final Answer:
The half-life of $^{137}Cs$ is approximately 30 years.