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SpyIntel [72]
3 years ago
7

The half-life of a certain element is 100 days. How many half-lives will it be before only one-eighth of this element remains?

Physics
1 answer:
Natalka [10]3 years ago
7 0

Answer:

3

Explanation:

The half-life is the time it takes for the amount of radioactive isotope to halve. Therefore, we have:

- After 1 half-life, only 1/2 of the element will be left

- After 2 half-lives, only 1/4 of the element will be left

- After 3 half-lives, only 1/8 of the element will be left

So, it will take 3 half-lives for the element to become 1/8 of its original amount.

Mathematically, this can be also verified by using the equation

\frac{N(t)}{N_0}=(\frac{1}{2})^\frac{t}{\tau_{1/2}}

where

N(t) is the amount of the element left at time t

N0 is the initial amount of the element

\tau_{1/2} is the half-life

Substituting t=3\tau_{1/2} (3 half-lives), we find

\frac{N(t)}{N_0}=(\frac{1}{2})^3=\frac{1}{8}

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