Answer:
Half life of the radioactive element is 5 days.
Step-by-step explanation:
Formula to get the final amount after the radioactive decay in 't' days,
[tex]A_t=A_0e^{-\lambda t}[/tex]
Here [tex]A_0[/tex] = Initial amount
λ = Decay constant
t = duration of decay
[tex]A_t[/tex] = Final amount
[tex]1000=100000e^{-\lambda(34)}[/tex]
0.01 = [tex]e^{-34\lambda}[/tex]
ln(0.01) = [tex]\text{ln}(-e^{34\lambda}})[/tex]
-4.6052 = -34λ
λ = 0.13544
Since, λ = [tex]\frac{\text{ln}(2)}{t_{\frac{1}{2}}}[/tex]
[tex]t_{\frac{1}{2}}=\frac{\text{ln}2}{0.13544}[/tex]
= 5.11
≈ 5 days
Therefore, half life of the radioactive element is 5 days.
