The half-life of an element is 5.8 &#x00D7;<!-- × --> 10 <mrow class="MJX-TeXAtom-OR

Kaiden Wilkins

Kaiden Wilkins

Answered question

2022-04-06

The half-life of an element is 5.8 × 10 11 . How long does it take a sample of the element to decay to 2 5 its original mass?

Answer & Explanation

Lucille Melton

Lucille Melton

Beginner2022-04-07Added 18 answers

In the question, the half-life should have units of time. Let's assume that the half-life is 5.8 × 10 11 s
In this case, the value of the rate constant is
k = ln 2 t 1 2 = ln 2 5.8 × 10 11 s = 1.20 × 10 12 s 1
Using the first equation, we can find the time, t at which the fraction of remaining atoms is 2 5 .
2 5 = e ( 1.20 × 10 12 s 1 ) t
t = 0.92 1.2 × 10 12 s 1 = 7.67 × 10 11 s
(or about 24,300 years)

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