The half-life of rubidium-87 (natural absorbance 27.83%) is 5.1x10^11 years. What mass of rubidium is present if an average sample decay rate of 35.0 disint./sec is detected?
I've already converted years to seconds but not sure what to do after..
Not sure what the absorbance has to do with things, but
a half-life of 5.1*10^11 years is a decay rate of
1.359*10^-10 % per year = 4.31*10^-18 % per second
so, if 35 per second is 4.31*10^-20 of the number of atoms, that means that you have
8.05*10^20 atoms, or 0.00133 moles
Not sure whether this helps ...
To calculate the mass of rubidium present, we need to use the decay rate, the half-life, and the natural absorbance of rubidium-87.
First, let's convert the decay rate from disintegrations per second to disintegrations per year. Since you have already converted years to seconds, we can directly use the value you obtained.
35.0 disintegrations/sec * (60 seconds * 60 minutes * 24 hours * 365.25 days) = X disintegrations/year
Once we have the decay rate in disintegrations per year, we can calculate the fraction of rubidium-87 atoms that decay in one year using the half-life.
Since the half-life of rubidium-87 is 5.1 x 10^11 years, we can calculate the fraction of rubidium-87 atoms that decay in one year:
Fraction decayed = 1 - (1/2)^(1/(half-life in years))
Fraction decayed = 1 - (1/2)^(1/(5.1 x 10^11))
Now, let's calculate the fraction of rubidium-87 atoms remaining in the sample after one year:
Fraction remaining = 1 - fraction decayed
Using the natural absorbance of rubidium-87 (27.83%), we can calculate the mass of rubidium present in the sample:
Mass of rubidium = (Fraction remaining) * (natural absorbance) * (total mass of the sample)
Please provide the total mass of the sample so we can proceed with the calculation.