Respuesta :
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 = [tex]\frac{1}{4}[/tex] = A'
We will use the following relation for calculating time elapsed in the decay
[tex]A' = A(\frac{1}{2} )^\frac{t}{t_1_/_2} }[/tex]
Thus,
[tex]\frac{1}{4} =1(\frac{1}{2} )^\frac{t}{3.8}[/tex]
We can write is as,
[tex](\frac{1}{2} )^2=(\frac{1}{2} )^\frac{t}{3.8}[/tex]
Since the base in both sides are equal, powers can also be equal and thus,
[tex]2=\frac{t}{3.8}[/tex]
So, t = 7.6 days
Answer: 7.64 days
Explanation: 1 -> 1/2 -> 1/4 Two half-life periods. Half-life = 3.823 2 x 3.823 = 7.64 d
