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Digiron [165]
3 years ago
5

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

Mathematics
1 answer:
Murrr4er [49]3 years ago
3 0

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,

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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