Answer:
8.625 grams of a 150 g sample of Thorium-234 would be left after 120.5 days
Explanation:
The nuclear half life represents the time taken for the initial amount of sample to reduce into half of its mass.
We have given that the half life of thorium-234 is 24.1 days. Then it takes 24.1 days for a Thorium-234 sample to reduced to half of its initial amount.
Initial amount of Thorium-234 available as per the question is 150 grams
So now we start with 150 grams of Thorium-234
[tex]150 \times \frac{1}{2}=24.1[/tex]
[tex]75 \times \frac{1}{2} =48.2[/tex]
[tex]34.5 \times \frac{1}{2} =72.3[/tex]
[tex]17.25 \times \frac{1}{2} =96.4[/tex]
[tex]8.625\times \frac{1}{2} =120.5[/tex]
So after 120.5 days the amount of sample that remains is 8.625g
In simpler way , we can use the below formula to find the sample left
[tex]A=A_{0} \cdot \frac{1}{2^{n}}[/tex]
Where
[tex]A_0[/tex] is the initial sample amount
n = the number of half-lives that pass in a given period of time.
