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Tom [10]
3 years ago
10

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

Chemistry
1 answer:
Arte-miy333 [17]3 years ago
5 0

Answer:

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 = \frac{1}{4} = A'

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

A' = A(\frac{1}{2} )^\frac{t}{t_1_/_2}  }

Thus,

\frac{1}{4} =1(\frac{1}{2} )^\frac{t}{3.8}

We can write is as,

(\frac{1}{2} )^2=(\frac{1}{2} )^\frac{t}{3.8}

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

2=\frac{t}{3.8}

So, t = 7.6 days

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