Final answer:
The number of atoms remaining after 1 hour and 24 minutes is 1789.
Step-by-step explanation:
The number of radioactive atoms remaining after a certain amount of time can be calculated using the formula:
N = N0 * (1/2)(t / T1/2)
Where N is the number of atoms remaining, N0 is the initial number of atoms, t is the time elapsed, and T1/2 is the half-life of the substance.
In this case, the initial number of atoms is 114500 and the half-life is 12 minutes. To find the number of atoms remaining after 1 hour and 24 minutes (which is equal to 84 minutes), substitute these values into the formula:
N = 114500 * (1/2)((84) / 12)
Simplifying the calculation gives:
N = 114500 * (1/2)7 = 1789 atoms