If a radiation source has an intensity of 650 rem at 1.0 m, what distance is needed to decrease the intensity of exposure to below 25 rem, the level at which no effects are detectable?

Verified step by step guidance

1. Understand that the intensity of radiation follows the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source. Mathematically, this is expressed as: $I\_1/I\_2\; =\; (d\_2/d\_1)^2$, where $I\_1$ and $I\_2$ are the intensities at distances $d\_1$ and $d\_2$, respectively.
2. Identify the given values: $I\_1\; =\; 650\; \backslash ,\; \backslash text\{rem\}$, $d\_1\; =\; 1.0\; \backslash ,\; \backslash text\{m\}$, and $I\_2\; =\; 25\; \backslash ,\; \backslash text\{rem\}$. The goal is to solve for $d\_2$, the distance at which the intensity is reduced to below 25 rem.
3. Rearrange the inverse square law formula to solve for $d\_2$: $d\_2\; =\; d\_1\; \backslash sqrt\{I\_1/I\_2\}$.
4. Substitute the known values into the formula: $d\_2\; =\; 1.0\; \backslash ,\; \backslash text\{m\}\; \backslash sqrt\{650\; \backslash ,\; \backslash text\{rem\}\; /\; 25\; \backslash ,\; \backslash text\{rem\}\}$. Simplify the ratio inside the square root.
5. Calculate the square root and multiply by $d\_1$ to find $d\_2$. This will give the distance at which the intensity is reduced to below 25 rem.

Key Concepts

Inverse Square Law

The Inverse Square Law states that the intensity of radiation decreases with the square of the distance from the source. This means that if you double the distance from the radiation source, the intensity of exposure is reduced to one-fourth. Understanding this principle is crucial for calculating how far one must be from a radiation source to achieve a desired intensity level.

Radiation Exposure Measurement

Radiation exposure is often measured in rems, which quantify the biological effect of ionizing radiation on human tissue. A level of 25 rem is considered the threshold below which no detectable effects occur. Familiarity with these units and their implications helps in assessing safety levels in radiation exposure scenarios.

Logarithmic Scale of Intensity

Radiation intensity often follows a logarithmic scale, meaning that small changes in distance can lead to significant changes in exposure levels. This concept is important when calculating the distance required to reduce exposure from a high level to a much lower one, as it emphasizes the non-linear relationship between distance and intensity.