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%.