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The concept of radioactive intensity refers to the strength of the radioactive source at a specific distance from it. Intensity tells us how much radiation is being emitted per unit area. In our problem, the initial intensity is given as 1.15 mrem/s路m虏. Simply put, this tells us how concentrated the radiation is when you are 0.50 meters away from the source.

Understanding intensity is important because it changes based on how far you are from the radioactive source. The farther you are, the more spread out the radiation becomes over a wider area, and hence, the intensity reduces. Always think of it as a flashlight beam getting dimmer as you move away. If you're too close, the radiation is stronger and more intense, but as you step back, it diminishes.

Remember, to change the intensity you experience, you can either move closer or farther from the source. Here, we are interested in reducing the intensity to make it safer for exposure.

Radiation exposure measures how much radiation a person might receive. It's crucial to understand because exposure affects our health. The dose you receive depends on the intensity of the source and how close you are to it. In this task, the desired exposure is 0.65 mrem/s路m虏. To achieve this safer level of exposure, the intensity has to drop from its initial value.

It's worth noting that exposure is cumulative, meaning that even if the intensity is lower, spending a longer time near the source can increase your total absorbed dose. Safety regulations dictate limits on how much exposure is permissible to avoid potential health risks such as radiation sickness.

Managing radiation exposure effectively means either lowering the intensity or increasing the distance, or ideally, a combination of both.

Calculating the correct distance to reduce the radiation intensity to a safe level involves applying the inverse square law. This is a crucial principle in radiation physics. The law states that the intensity of radiation decreases with the square of the distance from a source. In simple terms, if you double the distance from the source, the intensity quarters.

To find our specific distance, we use the formula: \[\frac{I_1}{I_2} = \frac{d_2^2}{d_1^2}\]Here, \(I_1\) is the initial intensity, \(I_2\) is the desired lower intensity, \(d_1\) is the initial distance, and \(d_2\) is what we want to calculate.

By solving \(d_2\) from \[d_2^2 = \frac{I_1}{I_2} \times (d_1)^2\]we get \(d_2 \approx 0.665 \text{ meters}\), meaning that moving to about 0.665 meters will safely lower the intensity to 0.65 mrem/s路m虏. This shows how even small adjustments in distance can significantly alter exposure levels and ensure safety.