The activity of a radioisotope is 3000 counts per minute at one time and 2736 counts per minute 48 hours later, then the half life time is 365 hours.
Half life time for the first order reaction will be calculated by uisng the below equation as:
k = 0.693/t, where
t = half life time
k is the rate constant and its value will be calculatedy using the below equation as:
ln(No/N) = kT, where
No = initial concentration of radioisotope = 3000
N = remaining contentration of radioisotope = 2736
T = time require for above change = 48 hours
On putting these values on above equation, we get
k = ln(3000/2736) / 48 = 0.0019
Now putting this value in the first equation, we get
t = 0.693/0.0019 = 364.7 = 365 hours
Hence half life time is 365 hours.
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