Problem: Consider this graph representing the decay of a radioactive nuclide.What is the half-life of the nuclide?

FREE Expert Solution

We’re being asked to determine the half-life of the nuclide using the graph representing the decay of a radioactive nuclide.


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln [N]t=-kt+ln [N]0


where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half

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Problem Details

Consider this graph representing the decay of a radioactive nuclide.
A graph of time, in years, versus number of nuclei. The graph starts in the upper left hand corner, representing one hundred percent of sample at time zero. The graph then decreases exponentially, approaching zero at t equals six thousand two hundred fifty years. The number of nuclei decreased by seventy five percent at t equals twenty five hundred years.

What is the half-life of the nuclide?

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What scientific concept do you need to know in order to solve this problem?

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