Question

Victor is using his Geiger-counter to record the amount of radiation that is leaking into the soil from a nearby nuclear disposal site. This radiation decreases by the square of the distance from the source. If he starts measurements 100 m from the disposal site how close will he need to stand if he hopes to measure soil with 4 times the radiation?
According to inverse square proportionality, measuring 4 times more radiation will require Victor to _____ his distance. Victor will need to stand _____ m from the disposal site. ​

Answer 1

If Victor starts measurements 100 m from the disposal site, he needs to stand 50 m from the source if he hopes to measure soil with 4 times the radiation.

I = 1 / r²

I = Intensity

r = Distance

At a distance of 100 m from the source,

I = 1 / 100²

I = 1 / 10000

I = $10^{-4}$ J / m² s

Four times this radiation will have an intensity of,

I = 4 * $10^{-4}$ J / m² s

4 * $10^{-4}$ = 1 / d²

d² = 1 / 4 * $10^{-4}$

d² = 0.25 * $10^{4}$

d = √ 25 * 10²

d = 5 * 10

d = 50 m

Therefore, he needs to stand 50 m from the source

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