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What will happen in a time of 7 hours, if a radioactive substance has an average life of 7 hours?
- a)Half of the active nuclei decay
- b)Less half of the active nuclei decay
- c)More than half of the active nuclei decay
- d)All active nuclei decay
Correct answer is option 'C'. Can you explain this answer?
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What will happen in a time of 7 hours, if a radioactive substance has ...
Explanation:
Radioactive decay follows an exponential decay law given by the equation:
N(t) = N₀e^(-λt)
where N(t) is the number of radioactive nuclei at time t, N₀ is the initial number of radioactive nuclei, λ is the decay constant, and e is the base of the natural logarithm.
The average life, also known as the half-life, is the time it takes for half of the radioactive nuclei to decay. It is given by the equation:
T₀.₅ = ln(2)/λ
where ln is the natural logarithm.
In this case, the average life is 7 hours, which means that T₀.₅ = 7 hours. Therefore, we can solve for λ:
λ = ln(2)/T₀.₅ = ln(2)/7 hours ≈ 0.099 hours^-1
Now, let's consider what happens in a time of 7 hours. We can use the radioactive decay equation to find the fraction of radioactive nuclei that decay in 7 hours:
N(7) = N₀e^(-λ * 7) ≈ 0.5N₀
This means that about half of the radioactive nuclei decay in 7 hours. However, this is just an average value. Some nuclei will decay earlier, and some will decay later. Therefore, the actual number of nuclei that decay in 7 hours may be more or less than half.
To answer the question, we need to compare the average life of 7 hours to the time of 7 hours. If the time is equal to the average life, then we expect half of the nuclei to decay. If the time is shorter than the average life, then we expect fewer than half of the nuclei to decay. If the time is longer than the average life, then we expect more than half of the nuclei to decay.
In this case, the time of 7 hours is equal to the average life of 7 hours. Therefore, we expect about half of the nuclei to decay. However, as mentioned earlier, the actual number of nuclei that decay in 7 hours may be more or less than half. Therefore, option C, "more than half of the active nuclei decay," is the correct answer.
Radioactive decay follows an exponential decay law given by the equation:
N(t) = N₀e^(-λt)
where N(t) is the number of radioactive nuclei at time t, N₀ is the initial number of radioactive nuclei, λ is the decay constant, and e is the base of the natural logarithm.
The average life, also known as the half-life, is the time it takes for half of the radioactive nuclei to decay. It is given by the equation:
T₀.₅ = ln(2)/λ
where ln is the natural logarithm.
In this case, the average life is 7 hours, which means that T₀.₅ = 7 hours. Therefore, we can solve for λ:
λ = ln(2)/T₀.₅ = ln(2)/7 hours ≈ 0.099 hours^-1
Now, let's consider what happens in a time of 7 hours. We can use the radioactive decay equation to find the fraction of radioactive nuclei that decay in 7 hours:
N(7) = N₀e^(-λ * 7) ≈ 0.5N₀
This means that about half of the radioactive nuclei decay in 7 hours. However, this is just an average value. Some nuclei will decay earlier, and some will decay later. Therefore, the actual number of nuclei that decay in 7 hours may be more or less than half.
To answer the question, we need to compare the average life of 7 hours to the time of 7 hours. If the time is equal to the average life, then we expect half of the nuclei to decay. If the time is shorter than the average life, then we expect fewer than half of the nuclei to decay. If the time is longer than the average life, then we expect more than half of the nuclei to decay.
In this case, the time of 7 hours is equal to the average life of 7 hours. Therefore, we expect about half of the nuclei to decay. However, as mentioned earlier, the actual number of nuclei that decay in 7 hours may be more or less than half. Therefore, option C, "more than half of the active nuclei decay," is the correct answer.
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What will happen in a time of 7 hours, if a radioactive substance has ...
In one average life, i.e. at 7 hours, 63.2 % of the active nuclei will decay. Therefore, in a time of 7 hours, it can be considered that more than half of the active nuclei will decay.
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What will happen in a time of 7 hours, if a radioactive substance has an average life of 7 hours?a)Half of the active nuclei decayb)Less half of the active nuclei decayc)More than half of the active nuclei decayd)All active nuclei decayCorrect answer is option 'C'. Can you explain this answer?
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Solutions for What will happen in a time of 7 hours, if a radioactive substance has an average life of 7 hours?a)Half of the active nuclei decayb)Less half of the active nuclei decayc)More than half of the active nuclei decayd)All active nuclei decayCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
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