Question

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

Answer 1

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