In 90 seconds, the mass of a radioactive element reduces to \(\frac{1}{16}\) of its original value. Determine the half- life of the element.
A
15.0s
B
18.0s
C
22.5s
D
30.0s
E
45.0s
Verified Correct Answer: C.
Physical Principles & Numerical Solution
\(\frac{1}{16} = (\frac{1}{2})^n\)
\((\frac{1}{2})^4 = (\frac{1}{2})^n\)
\(n = 4\)
90 secs = 4 half lives
1 half life = \(\frac{90}{4}\) secs
= 22.5 secs
Source: Myschool Past Questions Archive (Record #42932)