A selenium-75 source is producing 300 rem at a distance of 2.0 m?
b. What is its intensity at 25 m?

Verified step by step guidance

1. Step 1: Understand the problem. The intensity of radiation follows the inverse square law, which states that the intensity of radiation 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. Step 2: Identify the given values. From the problem, we know: $I\_1\; =\; 300\; \backslash ,\; \backslash text\{rem\}$, $d\_1\; =\; 2.0\; \backslash ,\; \backslash text\{m\}$, and $d\_2\; =\; 25\; \backslash ,\; \backslash text\{m\}$. We need to calculate $I\_2$, the intensity at 25 m.
3. Step 3: Rearrange the inverse square law formula to solve for $I\_2$. The formula becomes: $I\_2\; =\; I\_1\; \backslash cdot\; \backslash left(\backslash frac\{d\_1\}\{d\_2\}\backslash right)^2$.
4. Step 4: Substitute the known values into the formula. Replace $I\_1$ with 300 rem, $d\_1$ with 2.0 m, and $d\_2$ with 25 m. The equation becomes: $I\_2\; =\; 300\; \backslash cdot\; \backslash left(\backslash frac\{2.0\}\{25\}\backslash right)^2$.
5. Step 5: Simplify the expression to calculate $I\_2$. First, calculate the fraction $\backslash frac\{2.0\}\{25\}$, then square the result, and finally multiply by 300 to find the intensity at 25 m.

Key Concepts

Radiation Intensity

Radiation intensity refers to the power per unit area carried by a wave, typically measured in watts per square meter (W/m²). In the context of radiation sources, intensity decreases with distance from the source due to the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source.

Inverse Square Law

The inverse square law is a fundamental principle in physics that describes how a physical quantity (like light or radiation) decreases as the distance from the source increases. Specifically, if the distance from the source doubles, the intensity becomes one-fourth of its original value. This law is crucial for calculating changes in intensity at different distances.

Radiation Measurement Units

Radiation is often measured in units such as rem (roentgen equivalent man), which quantifies the biological effect of ionizing radiation on human tissue. Understanding these units is essential for interpreting radiation exposure and its potential health impacts, as well as for converting between different measurement systems when calculating intensity.