College

If the half-life of a radioactive isotope is 10 minutes, how long will it take for an 80 g sample to decay to 10 grams?

Answer :

If the half-life of a radioactive isotope is 10 minutes then it will take 30 minutes for an 80 g sample to decay to 10 grams.

What is half-life?

The phrase is frequently used in nuclear physics to refer to how long stable atoms last or how quickly unstable atoms decay radioactively. In a broader sense, the phrase is used to describe any kind of exponential decay.

The half-life of an element is given by the formula

N(t) = N(0) × [tex]0.5^{\frac{t}{T}}[/tex]

N(t) = remaining quantity of a substance after time t

N(0) = initial quantity of the substance

T = half-life

Given:

Half-life, T = 10 minutes

N(t) = 10 g

N(0) = 80g

So, according to the half-life formula

10 = 80 × [tex]0.5^{\frac{t}{10}}[/tex]

[tex]0.5^{\frac{t}{10}}[/tex] = 1/8

t = [tex]\frac{10ln(\frac{1}{8})}{ln(0.5)}[/tex]

t = 30 minutes

To know more about the half-life in a chemical reaction, visit:

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