A radioactive element has a half life of 4 days. The fraction that has decayed in 16 days is?
\(\frac{15}{16}\)
\(\frac{1}{16}\)
\(\frac{3}{4}\)
\(\frac{1}{4}\)
Explanation
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Note: Fraction left (Fr) is different from Fraction decayed (Fd):
Fr = 1/R (where R = 2^n)
n = t/T = 16/4 = 4 half lives
R = 2^4 = 16
Fr = 1/16
Fd = (R - 1)/R
= (16 - 1)/16 = 15/16
hence: The fraction that has decayed in 16 days is = 15 / 16 ===> Option A
What is actually making me angry is the fact that i actually recommended this site to my students i felt it helped me during mine.....while teaching them at home i've been noticing flaws like this....that is why i keep checking
Since the half-life of the radioactive element is 4 days, it means that after every 4 days, half of the remaining radioactive element will decay.
Let's assume that the initial amount of radioactive element is 1 unit. After the first 4 days, half of it will decay, and we will be left with 1/2 unit. After the second 4 days, half of the remaining 1/2 unit will decay, and we will be left with 1/4 unit. After the third 4 days, half of the remaining 1/4 unit will decay, and we will be left with 1/8 unit. Finally, after the fourth 4 days, half of the remaining 1/8 unit will decay, and we will be left with 1/16 unit.
Therefore, after 16 days, only 1/16 of the initial amount of the radioactive element will remain, and the fraction that has decayed is:
1 - 1/16 = 15/16
Therefore, the answer is (A) 15/16.
pls, something should be done about that 
Wrong,the question supposed to be find the atom for us to get 15/16.....the correct option for the question is B
Fraction remaining 1/2^n
Fr = 1/2^16÷4
Fr = 1/16
But here the question asked for fraction decayed .. which
Fd = 1- 1/16
Fd= 15/16
The right answer should be A
Pls make correction here
When I calculated it the answer was B not A and even if it is A i dont under how it was gotteb
