# It took 109.8 years for a 300.0 mg sample of an unknown radioactive material to completely disintegrate. Calculate the mass of the element (in grams/mole) assuming that the disintegrations per second are constant over the life-time of the sample, and the sample is labeled 100.0 Ci (Curie= 3.7x10^10 disintegrations per second)

This material has a half-life. It NEVER completely disintergrates.

That is what is written in the problem.

The assumptions here are wild.

OK. If all of the atoms are going to "disintegrate", and they do so at a "constant rate" independent of mass, then

Time= numberatoms/rate

The number of atoms= avagNumber*moles=
avagNumber*mass/molmass

and then you solve for molmass.

time= avagnumber*mass/molmass*rate

You are given time, avagnumber, mass, and rate. Make certain you have time and rate in consistent units.

## To solve this problem, we can use the formula:

Time (in seconds) = (Number of atoms / Rate of disintegrations per second)

We are given the following information:
- Time = 109.8 years = 109.8 × 365 × 24 × 60 × 60 seconds
- Rate = 100.0 Ci = 100.0 × 3.7 × 10^10 disintegrations per second

Now, let's calculate the number of atoms:
- Number of atoms = Avogadro's Number × Moles
- Moles = Mass / Molar mass

We are given the mass of the sample as 300.0 mg.

To calculate the molar mass, we need to find the moles using the mass and the molar mass formula:
Moles = Mass / Molar mass

Now we have all the information we need to plug into the equation:
Time = Avogadro's Number × (Mass / Molar mass) × Rate

Solving for the molar mass:
Molar mass = (Avogadro's Number × Mass × Rate) / Time

Plugging in the given values:
Molar mass = (6.022 × 10^23 atoms/mol × 300.0 mg × 100.0 × 3.7 × 10^10 disintegrations per second) / (109.8 × 365 × 24 × 60 × 60 seconds)

Now you can calculate the molar mass of the element by performing the above calculation.