Question

At time 0 seconds, activity of the radioactive material is $1600{\rm{ }}Bq$, at 8 seconds it becomes $100{\rm{ }}Bq$, then what is its activity at 2 seconds in Bq?
A. 400
B. 800
C. 200
D. 1200

Answer 1

The activity of the radioactive material reduces constantly but not linearly. Every material has its distinct half-life period and in that time period its activity level becomes half of the original. Half life is the most important phenomenon in the radioactive material.

Complete step by step answer:
As we have already mentioned, every radioactive material has its distinct half life period.
Now, the original activity level of the aforementioned material was $1600{\rm{ }}Bq$, initially.
At time $t{\rm{ }} = {\rm{ }}8s$, it reached to $100{\rm{ }}Bq$.
So, the final activity level is very less than half.
So, the material must have gone through several half life cycles.
Let us calculate the number of half life cycles.
$1600/2 = 800$ --- Cycle 1
$800/2 = 400$---- Cycle 2
$400/2 = 200$---- Cycle 3
$200/2 = 100$---- Cycle 4
So, it went through 4 half life cycles.
Time taken to go through 4 half life cycles is 8 seconds.
So, time for each half life cycle = $t = 8/4 = 2s$
So, the half life cycle of this radioactive material is 2 seconds.
So, in 2 seconds the activity level of the material will become half of the original, which is $800{\rm{}}Bq$.

Hence option B is correct.

Note: Half life cycle is extensively used in archeological studies. Scientists use the half-life of carbon-14 to determine the approximate age of organic objects. They determine how much of the carbon-14 has transformed. They can then calculate the age of a substance. The half life period of the carbon 14 is 5730 years. So, depending on the activity level in the carbon 14 from the very old objects/species, scientists can determine the age of that object/species.