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Half life of radioactive substance is 20 min. Difference between points of time when 33% disintegrate and 67% disintegrated is approximately1.) 10 min 2.) 20 min 3.) 30 min 4.) 40 min?
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Half life of radioactive substance is 20 min. Difference between point...
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Half life of radioactive substance is 20 min. Difference between point...
Explanation


The half-life of a radioactive substance is the time it takes for half of the substance to decay or disintegrate. In this case, the half-life is 20 minutes, which means that after 20 minutes, half of the substance would have disintegrated.


Calculating the time difference between 33% and 67% disintegration


To calculate the time difference between 33% and 67% disintegration, we need to first find out how long it takes for 33% and 67% of the substance to disintegrate. We can use the formula:


Amount remaining = Initial amount x (1/2)^(t/half-life)


where:



  • t = time elapsed

  • half-life = 20 minutes



Let's start with 33% disintegration:


0.33 = 1 x (1/2)^(t/20)


Take the natural logarithm of both sides:


ln(0.33) = (t/20) ln(1/2)


Solve for t:


t = 20 ln(0.33)/ln(1/2) ≈ 10.2 minutes


Now let's move on to 67% disintegration:


0.67 = 1 x (1/2)^(t/20)


Take the natural logarithm of both sides:


ln(0.67) = (t/20) ln(1/2)


Solve for t:


t = 20 ln(0.67)/ln(1/2) ≈ 22.8 minutes


Calculating the time difference


The difference between the two times is:


22.8 minutes - 10.2 minutes ≈ 12.6 minutes ≈ 13 minutes (rounded up)


Conclusion


The approximate time difference between 33% and 67% disintegration is 13 minutes. This means that it takes approximately 13 minutes for the substance to disintegrate from 33% to 67%.
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Half life of radioactive substance is 20 min. Difference between points of time when 33% disintegrate and 67% disintegrated is approximately1.) 10 min 2.) 20 min 3.) 30 min 4.) 40 min?
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