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
