A substance decays so that the amount a of the substance left after t years is given by: a = a 0 · (0.9) t, where a 0 is the original amount of the substance. what is the half-life (the amount of time that it takes to decay to half the original amount) of this substance rounded to the nearest tenth of a year?

Question

Samir Macias

Chemistry

14 August, 17:26

A substance decays so that the amount a of the substance left after t years is given by: a = a 0 · (0.9) t, where a 0 is the original amount of the substance. what is the half-life (the amount of time that it takes to decay to half the original amount) of this substance rounded to the nearest tenth of a year?

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Khalil · Answer 1

I think the correct form of the equation is given as:

a = a0 * (0.9) ^t

where t is an exponent of 0.9 since this is an exponential decay of 1st order reaction

Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:

a = 0.5 a0

Substituting this into the equation:

0.5 a0 = a0 * (0.9) ^t

0.5 = (0.9) ^t

Taking the log of both sides:

t log 0.9 = log 0.5

t = log 0.5 / log 0.9

t = 6.58 years

Answer:

half life = 6.58 years