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The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species?
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The radioactive element undergo 80 percent radioactive decay in 300 mi...
Calculation of Half-Life of a Radioactive Element
Radioactive decay is a process in which the nucleus of an unstable atom emits radiation in the form of alpha, beta, or gamma particles. The rate of radioactive decay is measured in half-life, which is the time taken for half of the radioactive nuclei to decay. In this problem, we are given that an element undergoes 80% radioactive decay in 300 minutes. We need to calculate the half-life of this species.
Understanding the Problem
Before we start calculating the half-life of the radioactive element, we need to understand the concept of radioactive decay and its mathematical expression. The rate of radioactive decay is given by the following equation:
N = N0e-λt
Where:
- N is the number of radioactive nuclei at time t
- N0 is the initial number of radioactive nuclei
- λ is the decay constant
- t is the time elapsed
Based on the given information, we know that 80% of the radioactive nuclei have decayed after 300 minutes. This means that:
N = 0.2N0
t = 300 minutes
Calculating Decay Constant
Using the equation for radioactive decay, we can solve for the decay constant λ:
N = N0e-λt
0.2N0 = N0e-λ(300)
e-λ(300) = 0.2
-λ(300) = ln(0.2)
λ = ln(5)/300
Calculating Half-Life
The half-life of a radioactive element is the time taken for half of the radioactive nuclei to decay. We can calculate the half-life using the following equation:
t1/2 = ln(2)/λ
Substituting the value of λ that we obtained earlier, we get:
t1/2 = ln(2)/(ln(5)/300)
t1/2 = 138.63 minutes
Conclusion
The half-life of the radioactive element is 138.63 minutes. This means that it takes 138.63 minutes for half of the radioactive nuclei to decay. The concept of radioactive decay and its mathematical expression are essential in understanding the behavior of radioactive elements and their applications in various fields, including medicine, energy, and environmental science.
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The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species?
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The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species?.
The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radioactive element undergo 80 percent radioactive decay in 300 min.calculate half life of this species?.
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