27Mg is a beta emitter and has a half-life of 9.458 minutes, while 241Am is an alpha emitter and has a half-life of 432.6 years.

a.      Write the radioactive decay reaction of 27Mg.

b.     Write the radioactive decay reaction of 241Am.

c.      What percentage of 241Am would remain after 1730 years? (hint: you had 100% initially)

d.     Initially, you have 15.0 µg of 27Mg. After 50.0 minutes, how much 27Mg remains?

e.      241Am is used as the detector in smoke detectors. How long would the smoke detector continue working (i.e., how long until the radiation fades into the background)? Assume that you diligently replace the 9V batteries every six months until this time.