# The number of a certain radioactive nuclide present in a sample decays from 160 to 20 in 30 minutes. What is the half-life of this radioactive species?

The equation for determining the half life of a radioactive species based on the decay rate is as follows:

t(1/2) = (t*ln2)/(ln(N(0)/N(t))

Where t(1/2) is the half life, N(0) is the initial quantity of the substance, and N(t) is the amount of substance remaining after t amount of time.  So...

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The equation for determining the half life of a radioactive species based on the decay rate is as follows:

t(1/2) = (t*ln2)/(ln(N(0)/N(t))

Where t(1/2) is the half life, N(0) is the initial quantity of the substance, and N(t) is the amount of substance remaining after t amount of time.  So we can input our specific values into the equation and solve for t(1/2).

t(1/2) = (30 min)(0.693)/(ln(160/20)) = 20.79/2.079 = 10 min

So the half life is 10 minutes.

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