# 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?

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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.**

The half-life of a radioactive element is the time needed for half of the material to decay.

Thus , let half life period is t minutes.

decay from 160 to 80 it needed t minutes.

decay from 80 to 40 it needed t minutes.

decay from 40 to 20 ,it neded t minutes.

So

decay from 160 to 20 ,it needed three half life periods ie. 3t minutes.

But we have given that from 160 to 20 ,it took time 30 minutes.

Thus

3t=30 min.

t=10 minutes.

**So half life period is 10 minutes for this particular substance**.