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A radioactive element undergoes 80% radioactive decay in 300 min. The half- life for this species in minutes is _________.
Correct answer is '129.15'. Can you explain this answer?
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Explanation:
- Radioactive decay is a process by which the nucleus of an unstable atom loses energy by emitting particles or electromagnetic radiation.
- The rate of radioactive decay is measured by the half-life of the radioactive element.
- Half-life is the time taken for half of the radioactive atoms to decay.
- The formula for half-life is given by:
- Where t1/2 is the half-life, λ is the decay constant, and ln is the natural logarithm.
- To find the half-life of the given radioactive element, we need to know the decay constant.
- The decay constant can be calculated using the formula:
- Where N0 is the initial number of radioactive atoms, Nt is the number of radioactive atoms at time t, and t is the time taken for decay.
- In this case, it is given that the radioactive element undergoes 80% decay in 300 min.
- This means that Nt = 0.2N0 (since 80% of the atoms have decayed).
- Substituting these values in the above formula, we get:
- Now we can use this value of λ to calculate the half-life using the formula:
- Substituting the value of λ, we get:
- Therefore, the half-life of the given radioactive element is 129.15 minutes.
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