Problem 83 - Chemistry Matter and Change

Question

Red blood cells A medical researcher is using a chromium- 51 source to study red blood cells. The gamma-emission intensity at a distance of 1.0 \(\mathrm{m}\) is 0.75 mrem \(/ \mathrm{s} \cdot \mathrm{m}^{2}\) At what distance would the intensity drop to 0.15 mrem \(/\) s.m \(^{2} ?\)

Step-by-Step Solution

Answer

The intensity will drop to 0.15 mrem/s*m^2 at a distance of approximately 2.236 meters when using the inverse square law formula: \(D2 = \sqrt{\frac{I1 \times D1^2}{I2}}\).

Step 1: Write down the initial information

We are given the following information: - Initial intensity (I1) = 0.75 mrem/s*m^2 at distance (D1) = 1.0 m - New intensity (I2) = 0.15 mrem/s*m^2, and we need to find the new distance (D2).

Step 2: Use the inverse square law formula

The inverse square law formula can be expressed as follows: \[I1 \times D1^2 = I2 \times D2^2\] We can rearrange this formula to find D2: \[D2 = \sqrt{\frac{I1 \times D1^2}{I2}}\]

Step 3: Substitute the given values and solve for D2

Now, we will substitute the given values into the formula: \[D2 = \sqrt{\frac{0.75 \times (1.0)^2}{0.15}}\] Simplify the expression: \[D2 = \sqrt{\frac{0.75}{0.15}}\]

Step 4: Calculate the new distance D2

By calculating the square root, we get: \[D2 = \sqrt{5}\] D2 ≈ 2.236 Hence, the intensity will drop to 0.15 mrem/s*m^2 at a distance of approximately 2.236 meters.

Key Concepts

Red Blood Cells

Red blood cells are crucial components of our blood. They are responsible for carrying oxygen from the lungs to the rest of the body and returning carbon dioxide back to the lungs. Without them, our cells wouldn't receive the oxygen they need to function.

These cells are unique because they lack a nucleus, which allows more room for hemoglobin, the protein that carries oxygen. Their biconcave shape increases the surface area for gas exchange, making them highly efficient in their role.

• Primary function: Transport oxygen and carbon dioxide.
• Structure: Biconcave and without a nucleus for more hemoglobin.
• Importance: Maintains oxygen delivery to all body parts.

Understanding how radiation affects red blood cells is key in medical research. Researchers use specific isotopes like chromium-51 to investigate these effects safely.

Radiation Intensity

Radiation intensity refers to the amount of radiation energy received per unit area. In medical research and diagnostics, controlling intensity is crucial to ensure safety and accuracy in measurements. By analyzing radiation intensity, scientists can make inferences about the source's strength and its effective range.

The gamma rays emitted by chromium-51, as used in the exercise, provide valuable insights into biological samples. It’s important to measure their intensity accurately to determine safe exposure levels.

• Key measurement: mrem/s*m² is a unit to express radiation intensity.
• Control: Essential for minimizing exposure in medical applications.
• Safety: Regular monitoring ensures non-harmful exposure levels.

Understanding intensity helps researchers make informed decisions about the safe handling of radioactive materials.

Distance Calculations

Distance calculations in physics often involve the inverse square law, especially when examining radiation. This law states that the intensity of a radiation source decreases with the square of the distance from the source. Essentially, if you double the distance from the source, the intensity becomes one-fourth.

In the exercise, the inverse square law formula is used to find the new distance at which radiation intensity drops to a certain level:

• Formula: \( I_1 \times D_1^2 = I_2 \times D_2^2 \).
• Rearrangement: Solve for the new distance \( D_2 = \sqrt{\frac{I_1 \times D_1^2}{I_2}} \).
• Application: Helps in determining safe distances from radioactive sources.

Such calculations are vital in fields such as radiology and nuclear medicine, where safety and precision are paramount.