Determine the total time that must elapse until only ¼ of an original sample of the radioisotope Rn-222 remains unchanged.

7.6 days

Explanation:

Radon is a radioactive element and Radon-222 is it's most stable isotope. The half-life of Radon-222 has been found to be approximately 3.8 days.

Let, the initial amount of the Rn-222 = 1 = A

Final amount = = A'

We will use the following relation for calculating time elapsed in the decay

Thus,

We can write is as,

Since the base in both sides are equal, powers can also be equal and thus,

So, t = 7.6 days

yes

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