Problema Solution
A radioactive element decays into non-radioactive substances. In 240days the radioactivity of a sample decreases by 41percent.
Give your answer to the following questions round to the nearest whole number of days.
(a) What is the half-life of the element?
half-life: (days)
(b) How long will it take for a sample of 100mg to decay to42mg?
time needed:
Answer provided by our tutors
Sample decays by 41% means that there is 100 - 41 = 59% radioactive substances left.
The function the describes the decay is:
f(t) = 0.5^(t/h), where h is the half-life, and t is the time passed
For t = 240 days we have f(240) = 0.59, that is:
0.5^(240/h) = 0.59
240/h = log(0.59)/log(0.5)
h = 240/(log(0.59)/log(0.5))
h = 315.29 days
The half-life in days is: 315 days.
Now lets find t so that f(t) = (42/100) that is
0.5^(t/315) = 0.42
.......
click here to see the equation solved for t
......
t = 394 days
The time needed is 394 days.