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Answering this question is one of the major successes of 20th-century physics. For strong decays, Gamow's alpha-tunneling model is quite successful. It relates the lifetime of an alpha emitter to the energy released in the decay using the approximately-valid assumption that nuclear density is constant and that the nucleus has a relatively sharp edge. For ...

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There is a thought experiment that might help the theoretician. Think of the nuclear attractive force as dynamic spatial field and the C14 atom as binding the two extra neutrons with this force field. Extremely rarely (avg. $4700$ years) there is weak spot in the containment field aligned with the neutron, and it escapes. You can build a simple 2D ...

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Actually, a nucleus has no electrons at all. The number of protons ($Z$) was never the same as the number of electrons (zero). Of course, most nuclei are part of complete atoms. If a nucleus that is part of an atom decays by alpha emission, it will typically also lose two electrons. That's not usually mentioned because it's not part of the radioactive decay ...

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Yes, the radiation both in Hiroshima and Nagasaki is very low, well, operationally non-existent. The radiation levels match the world average background radiation of 0.87 millisieverts per year. The bombs were optimized to have the maximum destructive power. That included a rather high altitude. The Hiroshima and Nagasaki bombs exploded in 580 and 500 ...

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From the Wikipedia article on the Trinity site where the first atomic bomb was tested. This is the same type of bomb as used over Nagasaki. More than seventy years after the test, residual radiation at the site is about ten times higher than normal background radiation in the area. The amount of radioactive exposure received during a one-hour visit ...

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A superconducting current loop could perhaps do the trick. Let's consider a very simplified analysis for creating a protective magnetic field for Venus. We're going to be essentially imitating earth's magnetic field. I don't know much about the solar wind, so I'll assume the strength varies per the inverse square law. Further, I assume the magnetic field ...

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The number of atoms in your radioactive sample falls exponentially with time, so we get something like: $$N = N_0 e^{-t/\tau}$$ where $\tau$ is a characteristic constant decay time called the mean lifetime. The half life is then defined by: $$\frac{1}{2} = e^{-t_{1/2}/\tau}$$ or: $$t_{1/2} = \tau\ln 2$$ By this reasoning a $3/4$ life would be ...

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Half life is a common physics misconception. Half life does not actually mean the cencentration of a substance being reduced to half by radio active disintegration. But it actially means the activity of the substance being reduced to half. For example if a sample of wood is found have uranium content with 5000 disintegration per second. And the half life is ...

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