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mariarad [96]
3 years ago
8

If a radioactive isotope has a half-life of 26.5 days, how many days does it take for a sample of the isotope to decrease by 35.

0% of its original value? View Available Hint(s) If a radioactive isotope has a half-life of 26.5 days, how many days does it take for a sample of the isotope to decrease by 35.0% of its original value? 40.1 days 16.5 days 7.15 days 0.0163 days
Chemistry
1 answer:
dangina [55]3 years ago
7 0

Answer:

16.5 days

Explanation:

Given that:

Half life = 26.5 days

t_{1/2}=\frac {ln\ 2}{k}

Where, k is rate constant

So,  

k=\frac {ln\ 2}{t_{1/2}}

k=\frac {ln\ 2}{26.5}\ days^{-1}

The rate constant, k = 0.02616 days⁻¹

Using integrated rate law for first order kinetics as:

[A_t]=[A_0]e^{-kt}

Where,  

[A_t] is the concentration at time t

[A_0] is the initial concentration

Given:

35.0 % is decomposed which means that 0.35 of [A_0] is decomposed. So,

\frac {[A_t]}{[A_0]} = 1 - 0.35 = 0.65

t = 7.8 min

\frac {[A_t]}{[A_0]}=e^{-k\times t}

0.65=e^{-0.02616\times t}

<u>t = 16.5 days.</u>

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