A β-emitting radiation source gives 250 units of radiation at a distance of 4.0 m. At what distance does the radiation drop to one-tenth its original value?

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.
2. Set up the equation using the inverse square law: \( I_1 \times d_1^2 = I_2 \times d_2^2 \), where \( I_1 \) is the initial intensity, \( d_1 \) is the initial distance, \( I_2 \) is the final intensity, and \( d_2 \) is the final distance.
3. Substitute the given values into the equation: \( 250 \times (4.0)^2 = (250/10) \times d_2^2 \).
4. Simplify the equation to solve for \( d_2^2 \).
5. Take the square root of both sides to find \( d_2 \), the distance at which the radiation intensity is one-tenth of its original value.

Key Concepts

Beta Radiation

Beta radiation consists of high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei. Understanding beta radiation is crucial as it helps in analyzing how this type of radiation interacts with matter and how its intensity diminishes with distance.

Inverse Square Law

The inverse square law states that the intensity of radiation from a point source decreases with the square of the distance from the source. This principle is essential for calculating how radiation levels change as one moves away from the source, which is key to solving the given problem.

Half-Life and Decay

Half-life is the time required for half of the radioactive atoms in a sample to decay. While the question specifically asks for a drop to one-tenth of the original value, understanding half-life and decay processes is important for grasping how radiation levels decrease over time and distance.