Answered

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You have 134,720 grams of a radioactive kind of actinium. How much will be left after 50 days if its half-life is 10 days?

Sagot :

Given:

The initial quantity of the actinium that will decay is 134720 grams.

Time, t=50 days

The half-life of the decaying quantity is 10 days.

To find the quantity that still remains after time t:

The half-life formula is given by,

[tex]N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}}[/tex]

On substitution we get,

[tex]\begin{gathered} N(50)=134720(\frac{1}{2})^{\frac{50}{10}} \\ =134720\times(\frac{1}{2})^5 \\ =134720\times0.03125 \\ =4210\text{ grams} \end{gathered}[/tex]

Hence, the quantity that still remains after time 50 days is 4210 grams.

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