The half life period of a radioactive element is 27.96 days. Calculate the time taken by a given sample to reduce to 1/8th of its initial activity

You need k.

k = 0.693/t1/2</su>

Then ln(No/N) = kt
Set No = 100
Set N = 100*1/8 =?
k from above.
Solve for t in days.

To calculate the time taken by a sample to reduce to 1/8th of its initial activity, we need to use the concept of half-life.

The half-life is the time it takes for half of a sample of a radioactive substance to decay or lose its activity. In this case, we know that the half-life period of the radioactive element is 27.96 days.

Since we want to determine the time taken for the sample to reduce to 1/8th of its initial activity, we need to find the number of half-lives it takes for the sample to reach that point.

To do this, start by setting up an equation:

(1/2) ^ n = 1/8,
where n is the number of half-lives.

Now, let's solve for n:

(1/2) ^ n = 1/2^3,
since 1/8 = 1/2^3

Rewriting the equation, we have:

1/2^3 = 1/2^n.

Comparing the exponents, we get:

n = 3.

Therefore, it takes 3 half-lives for the sample to reduce to 1/8th of its initial activity.

Now, to determine the time taken, we multiply the number of half-lives by the half-life period:

Time taken = n * half-life period = 3 * 27.96 days = 83.88 days.

So, the time taken by the given sample to reduce to 1/8th of its initial activity is approximately 83.88 days.