Answer :
The half life of the substance is 828.37
What is Half life?
The period of time it takes for one-half of a radioactive isotope to decay is known as the half-life. An individual radioactive isotope's half-life is unaffected by environmental factors and is independent of the isotope's starting concentration.
The amount of time needed for half of a radioactive sample's atomic nuclei to decay
Given:
As, The amount of a substance after t days is given by:
p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]
Original amount after 300 days.
p(300)= 0.778p(0).
p(t)= [tex]p(0)[/tex][tex]e^{-kt[/tex]
0.778 = p(0)[tex]e^{-300k[/tex]
-300k= log (0.778)
-300k= -0.109020
k = 0.0003634
So, p(t)= [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]
This is t for which P(t) = 0.5P(0). So
0.5p(0)= [tex]p(0)[/tex][tex]e^{-0.0003634t[/tex]
[tex]e^{-0.0003634t[/tex] = 0.5
log ( [tex]e^{-0.0003634t[/tex]) = log 0.5
-0.0003634 t = log 0.5
t= -0.30102999566/ -0.0003634
t= 828.37
Hence, the half life of the substance is 828.37
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