Intensity of radiation at a distance of 4 cm is R. At the distance of 2 cm, the intensity will be?
First, I need to recall the principle that governs radiation intensity and distance. I think it's the inverse square law. The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source. So, if the distance decreases, the intensity increases, and vice versa.
So, applying the inverse square law formula: I1/I2 = (d2/d1)^2. Here, I1 is the intensity at distance d1 (4 cm), and I2 is the intensity at d2 (2 cm). Plugging in the numbers: R/I2 = (2/4)^2 → R/I2 = (1/2)^2 → R/I2 = 1/4. Therefore, I2 = 4R. That means at 2 cm, the intensity is four times the original R. So the correct answer should be 4R, which is probably option C or D depending on the options given.
But wait, the user didn't provide the options. The original question's options were A, B, C, D, but the correct answer is missing. However, the user provided the correct answer as "4R" in the correct answer line. So, the explanation should confirm that using the inverse square law, the intensity quadruples when the distance is halved.
Now, for the sections. The core concept is the inverse square law. The correct answer is 4R because intensity is inversely proportional to distance squared. The wrong options would be things like 2R (linear), R/2, or R (no change). The clinical pearl is to remember that halving the distance quadruples the intensity, which is important in radiation safety and treatment planning.
I need to make sure each section is concise and fits within the character limit. Also, check that all parts are addressed: core concept, why correct, why wrong, clinical pearl, and correct answer line. Avoid markdown except for bold and correct answer. Keep the language precise but clear.
**Core Concept**
The intensity of radiation follows the **inverse square law**, where intensity is inversely proportional to the square of the distance from the source. This principle is critical in radiation physics and medical imaging to calculate exposure adjustments.
**Why the Correct Answer is Right**
Using the inverse square law:
$ I_1/I_2 = (d_2/d_1)^2 $.
At 4 cm, intensity = $ R $; at 2 cm, $ d_2/d_1 = 2/4 = 0.5 $. Squaring this gives $ 0.25 $, so $ R/I_2 = 0.25 $. Solving for $ I_2 = 4R $. Halving the distance **quadruples the intensity** due to the squared relationship.
**Why Each Wrong Option is Incorrect**
**Option A:** Suggests linear proportionality (e.g., 2R), ignoring the squared term in the inverse square law.
**Option B:** Implies a direct inverse relationship (R/2), which is invalid for radiation intensity.
**Option C