Question

Po−218 is an alpha emitter with a half-life of 3.0 minutes. if a sample contains 59 mg of po−218, how many alpha emissions would occur in 9.0 minutes?

Answer 1

1.4x10^20 alpha emissions. First, determine how many atoms of Po-218 you have. Do this by dividing the mass by 218 to get the number of moles, then multiply by Avogadro's number: 0.059 g / 218 g/mol * 6.0221409x10^23 atoms/mol = 1.63x10^20 atoms. Now we need to figure out how many half lives we're going to be observing the polonium. So take the time that we'll be observing and divide by the half life. So 9.0 / 3.0 = 3.0 So we're going to be spending 3 half lives. That means that only 2^-3, or 0.125 = 12.5 percent of the original polonium will be left. Which means that 100% - 12.5% = 87.5% of the atoms will have decayed. So let's figure that out. 0.875 * 1.63x10^20 = 1.43x10^20 Rounding to 2 significant figures gives 1.4x10^20 alpha emissions.