A radioactive atom decays 10% of radioactivity in every 40 minutes. If the current radioactivity of the atom is 35 curie, find what will be its reactivity after 2 hours?
1. 22.9 curie
2. 23.9 curie
3. 19.9 curie
4. 20.9 curie
1. 22.9 curie
2. 23.9 curie
3. 19.9 curie
4. 20.9 curie
Correct Answer – Option 1 : 22.9 curie
Given:
Radioactivity of the atom = 35 curie
Decay rate = 10% of present reactivity
Concept:
Since, the candle loses its length after 40 minutes seconds, so it will lose its reactivity 3 times in 2 hours. Use successive decrease percentage formula to calculate the reactivity after 2 hours.
Calculation:
% decrease in reactivity after 40 minutes;
= -10 -10 + (100/100)
= -19%
% decrease after 80 seconds;
= – 19 – 10 + (19 × 10)/100
= -29 + 1.9
= 27.1%
% decrease after 120 seconds;
= – 27.1 – 10 + (27.1 × 10)/100
= – 37.1 + 2.71
= 34.39%
∴ % decrease in radioactivity after 120 minutes = 34.39%
Radioactivity after 120 minutes = 100% – 34.39% = 65.61% of 35 curie
= 22.9 curie