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enter image description here What does safety limit mean here?

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closed as off-topic by John Rennie, StephenG, user259412, Jon Custer, ZeroTheHero Jun 6 at 11:07

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  • $\begingroup$ Think of it as decays per second. $\endgroup$ – MaxW Jun 2 at 16:10
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    $\begingroup$ In the context of the question it simply doesn't matter what the phrase means. We could write "The radiation emitted by a source of half-life 3 hrs is 32 times [some arbitrary value]. Minimum time for the radiation to be under the [arbitrary value] is:" and the question would be the same. $\endgroup$ – dmckee Jun 2 at 17:24
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    $\begingroup$ Typically, the safety limits is not defined in decay/seconds, but in Sv/hr. I.e. not the decay rate of the source is limited, but the energy of the poeple around it, what they get in the form of ionizing radiation per time unit (weighted with various biological parameters). However, in this example, the problem description is clearly about the source. It is a super-trivial task. $32=2^5$, so the half life must be spent 5 times to get the radiation below the limit. $3\cdot 5=15$, so (c) is the solution. $\endgroup$ – user259412 Jun 2 at 22:35
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The safety limit there is the limit above which ionising radiation can cause serious damage to matter, particularly living tissues. Crossing this limit is dangerous, making it necessary to control our exposure to such radiation.

Now, in case you are also looking for some explanation for the answer:

For that problem, you don't really need to know much about what exactly the safety limit is, just that it exists and that after a half-life a source will emit, on average, half the radiation it was emitting at the start.

Therefore, after one half-life, the radiation will still be 16 times above the safety limit. After 5 half-lives, or 15 hours, the radiation will have halved 5 times, going from 32 $\rightarrow$ 16 $\rightarrow$ 8 $\rightarrow$ 4 $\rightarrow$ 2 $\rightarrow$ 1, which means the radiation is right around its safety limit.

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