Question

A radio active isotope decays according to the exponential decay equation where t is in days. For the half life: The half life is the solution (t) of the equation : a2=ae−9.753t

Answer 1

A radioactive material is an element that is highly unstable due to its high neutron-to-proton ratio. Because of this, they spontaneously undergo nuclear reaction under nuclear fission releasing subparticles. The time it took to consume half of the original amount of the radioactive material is called the half-life.

The equation is a2=ae^(−9.753t), where a2 is the concentration after time t and a is the original concentration. The ratio of a2/a should be 0.5/1 or 1/2. Therefore,
a2/a = e^(-9.753t)
0.5 = e^(-9.753t)
ln(0.5) = lne^(-9.753t)
ln(0.5) = -9.753t
t = 0.071 days or 1.7 hours.