kristenholloway
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The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 220 grams of a radioactive isotope, how much will be left after 5 half-lives?
Use the calculator provided and round your answer to the nearest gram.

Respuesta :

wolf1728
220 grams
After 5 half-lives you have (1 / (2^5) ) of the original remaining.
2^5 = 32
So, 1/32 = 0.03125
220 * .03125 = 6.875 grams remaining after 5 half-lives.

After 5 half-lives, the 7 grams of radioactive isotope will be left if the starting with 220 grams of a radioactive isotope.

What is exponential decay?

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

If we start with 220 grams of a radioactive isotope, after one half-life the quantity will diminish to 220/2 = 110 grams

This can be written as:

[tex]\rm = 220(\dfrac{1}{2})^1[/tex]

After second half:

[tex]\rm = 220(\dfrac{1}{2})^2[/tex]

Similarly, after 5 half-lives:

[tex]\rm = 220(\dfrac{1}{2})^5[/tex]

= 6.875 grams ≈ 7 grams

Thus, after 5 half-lives the 7 grams of radioactive isotope will be left if the starting with 220 grams of a radioactive isotope.

Learn more about the exponential decay here:

brainly.com/question/14355665

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