Radium-226 is radioactive and has a half life of 1600. years. How much of a 9.70mg sample would be left after ×6.01103 years?Round your answer to 2 significant digits. Also, be sure your answer has a unit symbol.
Question
Radium-226 is radioactive and has a half life of 1600. years. How much of a 9.70mg sample would be left after ×6.01103 years?Round your answer to 2 significant digits. Also, be sure your answer has a unit symbol.
Solution
To solve this problem, we need to use the formula for radioactive decay which is:
N = N0 * (1/2)^(t/T)
where: N is the final quantity of the substance N0 is the initial quantity of the substance t is the time that has passed T is the half-life of the substance
Given: N0 = 9.70 mg t = 6.01103 years T = 1600 years
We can substitute these values into the formula:
N = 9.70 mg * (1/2)^(6.01103/1600)
Now, we just need to calculate the value of N.
N = 9.70 mg * (1/2)^(0.003757)
N = 9.70 mg * 0.997
N = 9.67 mg
So, after 6.01103 years, there would be approximately 9.67 mg of the Radium-226 sample left.
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