(Solved): pls show your work In 1898, Marie and Pierre Curie discovered radium in a mineral pitchblende sampl ...

In 1898, Marie and Pierre Curie discovered radium in a mineral pitchblende sample (i.e., uraninite). The most staple isotope of radium, radium-226 $$\left({}^{226}\mathrm{Ra}\right)$$, has a half-life of 1600 years and was commonly used for a variety of commercial applications until it was deemed toxic to humans. (a) Determine the binding energy per nucleon for this radium isotope given that its isotopic mass is $$226.0254098\mathrm{u}$$. (b) Radium-226 decays to Radon- 222 by the emission of an alpha particle. The corresponding decay process is described by the reaction $${}^{226}\mathrm{Ra}?{}^{22}\mathrm{Rn}+?$$ Determine the maximum energy (in MeV) transferred to the alpha particle during this reaction given that $$m\left({}^{226}\mathrm{Ra}\right)=226.0254098\mathrm{u},m\left({}^{222}\mathrm{Rn}\right)=222.0175763\mathrm{u}$$, and $$m(?)=4.0015062\mathrm{u}$$. (c) Radium-226 was formerly used in self-luminous paints for watches, clocks, switches, and instrument dials. A typical self-luminous watch dial with radium paint contained approximately $$1?\mathrm{g}$$ of radium. Determine the initial activity of a typical watch dial in units of $$\mathrm{Bq}$$ and $$\mathrm{Ci}$$. (d) Assuming that watch dial was painted with radium in 1920, determine the activity (in $$\mathrm{Bq}$$ and $$\mathrm{Ci}$$ ) of that dial in the year 2023.