The isotopic mass of 210 rn 86 is 209.989669 amu. when this nuclide decays by electron capture, it emits 2.368 mev. what is the isotopic mass of the resulting nuclide?

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The element here is Radon (Rn) with atomic number of 86. To solve this. add the mass of an electron to the isotopic mass (due to electron capture). Then, from here, subtract the corresponding mass of gamma radiation. (931 mev = 1 amu)

*mass of electron = 0.00054858 amu

isotopic mass = (209.989669 amu + 0.00054858 amu) - 2.368 mev*(1 amu/931 mev)

isotopic mass = 209.9876741 amu

They can measure  the amount of energy gained or lost