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After 45 hours, how many grams of the imaginary element 317-Bulldogs will be left if the original sample was 400 grams and the half-life (t1/2) is 9 hour

After 45 Hours How Many Grams Of The Imaginary Element 317Bulldogs Will Be Left If The Original Sample Was 400 Grams And The Halflife T12 Is 9 Hour class=

Sagot :

We know that:

- the original sample was 400 grams

- the half-life (t1/2) is 9 hours

And we must find how many grams of the imaginary element 317-Bulldogs will be left after 45 hours.

To find it, we need to know that

And to determine the amount of a radioactive isotope remaining after a given number half-lives we can use the next formula:

[tex]\text{ amount remaining}=\text{ initial amount}\times(\frac{1}{2})^n[/tex]

Where n is the number of half-lives.

Now, to use the formula we need calculate n

[tex]n=\frac{\text{ time passed}}{\text{ half life}}=\frac{45\text{ hours}}{9\text{ hours}}=5\text{ hours}[/tex]

Then, having that n = 5 we can replace the values in the formula for the amount remaining

[tex]\text{ amount remaining}=400\cdot(\frac{1}{2})^5=12.5g[/tex]

ANSWER:

There would be 12.5 grams left of 317-Bulldogs after 45 hours

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