Answer:
3.12 kg.
Step-by-step explanation:
Mass after t years:
The mass of the elements after t years is given by the following equation:
[tex]M(t) = M(0)(1-r)^t[/tex]
In which M(0) is the initial mass and r is the decay rate, as a decimal.
The half life of Cs-137 is 30.2 years.
This means that:
[tex]M(30.2) = 0.5M(0)[/tex]
We use this to find r.
[tex]M(t) = M(0)(1-r)^t[/tex]
[tex]0.5 = M(0)(1-r)^{30.2}[/tex]
[tex](1-r)^{30.2} = 0.5[/tex]
[tex]\sqrt[30.2]{(1-r)^{30.2}} = \sqrt[30.2]{0.5}[/tex]
[tex]1 - r = 0.5^{\frac{1}{30.2}}[/tex]
[tex]1 - r = 0.9773[/tex]
So
[tex]M(t) = M(0)(0.9773)^{t}[/tex]
If the initial mass of the sample is 100kg, how much will remain after 151 years?
This is M(151), with M(0) = 100. So
[tex]M(t) = 100(0.9773)^{t}[/tex]
[tex]M(151) = 100(0.9773)^{151} = 3.12[/tex]
The answer is 3.12 kg.
