Calculate the time in which the activity of an element is reduced to 90% of its original value. The half-life period of the element is 1.4*10^10 years . Answer :- 2.13*10^9 years
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To calculate the time it takes for the activity of an element to be reduced to 90% of its original value, we can use the concept of half-life.
The half-life of a radioactive element is the time it takes for half of the original amount of the element to decay. In this case, the half-life of the element is given as 1.4*10^10 years.
First, let's determine the number of half-lives needed for the activity to be reduced to 90%. We can calculate this by dividing the time passed by the half-life.
Number of half-lives = (log(Initial Activity / Final Activity) / log(2))
In this case, the initial activity is 100% and the final activity is 90%. So, the equation becomes:
Number of half-lives = (log(1 / 0.9) / log(2))
Next, we can calculate the time it takes for the activity to be reduced to 90% by multiplying the number of half-lives by the half-life period.
Time = Number of half-lives * Half-life period
Substituting the values, we get:
Time = [(log(1 / 0.9) / log(2))] * (1.4 * 10^10 years)
Calculating this, we find:
Time ≈ 2.13 * 10^9 years
So, the time it takes for the activity of the element to be reduced to 90% of its original value is approximately 2.13 * 10^9 years.