The half life is 0.47906yr
The uncertainty principle governs radioactive decay, making it impossible to predict with precision when a given nucleus will split apart and release a particle.
However, we can estimate the likelihood that a nucleus will dissolve in a specific amount of time.
We can foretell what portion of a huge number of nuclei will dissolve during that time.
Regardless of the isotope's quantity, this fraction will fluctuate based on each isotope's stability.
Alternatively, we can consider the issue in terms of how long it will take a specific fraction of an isotope to dissociate.
We have r0 = 6608 min–1 g–1, while r = 2932 min–1 g–1, and t = 7.29 days. Substituting into
we then have
ln r/r0 = −0.693*t / t1/2
ln (2932/6603) = -0.693 * 7.29 / t1/2
ln (0.44404) = -0.693*7.29/t1/2
t1/2 = (-0.693/-0.8118) * 7.29days
t1/2= 0.8536*7.29days
1yr = 28.1yrs
0.0199yr (7.29days) = 0.56123yr
t1/2 = 0.8536*0.56123
Half Life = 0.47906yr.
Hence the half life is 0.47906yr
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