Mathematics: A certain radioactive substance decays from 100000 grams to 1000 grams in 34 days. What s it s half-life ?

A certain radioactive substance decays from 100000 - id10000010606599, dbenitezmontoya3

Aneesa2507

17.03.2022

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,

$A_t=A_0e^{-\lambda t}$

Here A_0 = Initial amount

λ = Decay constant

t = duration of decay

A_t = Final amount

$1000=100000e^{-\lambda(34)}$

0.01 = $e^{-34\lambda}$

ln(0.01) = $\text{ln}(-e^{34\lambda}})$

-4.6052 = -34λ

λ = 0.13544

Since, λ = $\frac{\text{ln}(2)}{t_{\frac{1}{2}}}$

$t_{\frac{1}{2}}=\frac{\text{ln}2}{0.13544}$

= 5.11

≈ 5 days

Therefore, half life of the radioactive element is 5 days.

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