How much time would it take for 12000 atoms of nitrogen-13 (half-life is 7.13 s) to decay to 750 atoms?
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28.52 seconds

Initial number of atoms of Nitrogen 12,000 atoms

Half-life = 7.13

Number of atoms after decay = 750 atoms

We are required to determine the time taken for the decay.

Note that half life is the time taken for a radioactive isotope to decay to a half of its original amount.

Using the formula;

Remaining amount = Initial amount × (1/2)^n , where n is the number of half lives

In our case;

750 atoms = 12,000 atoms × (1/2)^n

0.0625 = 0.5^n

n = log 0.0625 ÷ log 0.5

n = 4

But, 1 half life =7.13 seconds

Therefore;

Time taken = 7.13 seconds × 4

                  = 28.52 seconds

Therefore, the time taken for 12,000 atoms of nitrogen to decay to 750 atoms is 28.52 seconds

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