Find out the answer to "What is the half life decay rate formula?"

Sappeycuii

Answered question

2022-05-14

What is the half life decay rate formula?

Calvin Oneill

Beginner2022-05-15Added 20 answers

If we start from an initial concentration of A, it is

[A]_{0}

. Then, it approaches a final concentration [A] that is half in quantity.
Therefore, the first half-life is written as

[A] = \frac{1}{2} [A]_{0}

To find further half-lives, keep halving the concentration n times. So, we would have:

[A] = [A]_{0} * \frac{1}{2} * \frac{1}{2}

[A] = [A]_{0} (\frac{1}{2})^{n}

If we want to determine the number of half-lives n, then we can use the total time passed t and divide by the half-life

t_{1 / 2}

.
So, we could write this in a more convenient form as

[A] = [A]_{0} (\frac{1}{2})^{t / t_{1 / 2}}

Or, in a more universal form, since [A] and

[A]_{0}

have the same units, we could easily just call the quantity of the decaying substance as a function of time N(t) to get

N (t) = N_{0} (\frac{1}{2})^{t / t_{1 / 2}}

where N can be atoms, grams, mols, whatever.

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