Answer:
There will be 8 grams left after 36 minutes.
Step-by-step explanation:
A half-life is how long it takes for half of the amount to go away. In this case, we see that we have two half-life periods worth, which you can determine by dividing the total time by the half-life time.
36mins/16mins = 2 half lives.
Now we can raise 1/2 to the power of how many half lives we have (2). Then we multiply that by the amount in the sample.
(1/2)^2 * 36
1/4 * 36
8 grams
There are 8 grams that will be left after 36 minutes if you start with 32 grams of it.
Given
The half-life of a radioactive kind of element is 18 minutes.
The half-life is the amount of time it takes for a given isotope to lose half of its radioactivity.
The half-life of the radioactive kind of element is given by;
[tex]\rm N = N_0\left (\dfrac{1}{2}\right )^{\dfrac{t}{t^{1/2}}}[/tex]
Where
No = Initial amount
t = time elapsed
t½ = Half life
N = Amount of substance left.
Substitute all the values in the formula;
[tex]\rm N = N_0\left (\dfrac{1}{2}\right )^{\dfrac{t}{t^{1/2}}}\\\\N= 32 \times \left (\dfrac{1}{2 }\right )^{\dfrac{36}{18}}\\\\N = 32 \times \left (\dfrac{1}{2 }\right )^2\\\\N=32 \times \dfrac{1}{4}\\\\N = 8[/tex]
Hence, there are 8 grams will be left after 36 minutes, if you start with 32 grams of it.
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