A shielded γ-ray source yields a dose rate of 0.052 rad / h at a distance of 1.0 m for an averag

step 1 First question, we first want to find what is the allowed dose based on the setting that we have

A shielded γ-ray source yields a dose rate of 0.052 rad / h...

A shielded $\gamma$ -ray source yields a dose rate of 0.052 $\mathrm{rad} / \mathrm{h}$ at a distance of 1.0 $\mathrm{m}$ for an average-sized person. If workers are allowed a maximum dose of 5.0 $\mathrm{rem}$ in 1 year, how close to the source may they operate, assuming a $40-\mathrm{h}$ work week? Assume that the intensity of radiation falls off as the square of the distance. (It actually falls off more rapidly than 1$/ r^{2}$ because of absorption in the air, so your answer will give a better-than-permissible value.)

A shielded $\gamma$ -ray source yields a dose rate of 0.052 $\mathrm{rad} / \mathrm{h}$
at a distance of 1.0 $\mathrm{m}$ for an average-sized person.
If workers are allowed a maximum dose of 5.0 $\mathrm{rem}$ in
1 year, how close to the source may they operate, assuming
a $40-\mathrm{h}$ work week? Assume that the intensity of radiation
falls off as the square of the distance. (It actually falls off
more rapidly than 1$/ r^{2}$ because of absorption in the air,
so your answer will give a better-than-permissible value.)

Key Concepts

Inverse Square Law

This is the principle stating that the intensity of radiation (or any point-source emission) decreases in proportion to the square of the distance from the source. In practical terms, if you double the distance from the source, the dose rate or intensity becomes one-fourth of its initial value. This concept is fundamental in radiation protection for determining safe distances relative to a radioactive source.

Radiation Dosimetry

Radiation dosimetry involves measuring and calculating the absorbed dose of radiation. In this context, units such as rad and rem are used to quantify the dose, where 1 rad represents the absorption of a specific amount of radiation energy per unit mass, and rem accounts for the biological effect of that radiation. Understanding these units is crucial for ensuring that exposure remains within safe limits.

Occupational Exposure Limits

Occupational exposure limits define the maximum radiation dose that workers are permitted to receive within a given period, usually to minimize health risks. These limits are established by regulatory authorities and are critical in planning safe working practices in environments where radiation is present, ensuring workers do not exceed the cumulative allowable dose over time.

Exposure Time Calculation

Exposure time calculations combine the dose rate with the duration of exposure to determine the total received dose. For instance, knowing the dose rate in rad per hour and the number of hours worked per week or year allows one to calculate whether the cumulative dose stays within the permissible limits, thereby informing decisions on safe operating distances or required protective measures.

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