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A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .?
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A radioactive sample decays to 10% of its initial amount in 5600 minut...
Radiation Decay
In radioactive decay, the amount of a radioactive substance decreases over time due to the spontaneous disintegration of its atomic nuclei. This process follows an exponential decay model, which can be described by the equation:
N(t) = N₀ * e^(-kt)
- N(t) represents the quantity of the substance at time t.
- N₀ is the initial quantity of the substance.
- k is the rate constant, which determines the speed of decay.
- e is the base of the natural logarithm (~2.71828).
- t is the time elapsed.
Finding the Rate Constant
To find the rate constant, we need to use the given information that the sample decays to 10% (0.1) of its initial amount in 5600 minutes. We can substitute these values into the exponential decay equation:
0.1 = N₀ * e^(-k * 5600)
We can simplify this equation by dividing both sides by N₀:
0.1 / N₀ = e^(-k * 5600)
Next, we can take the natural logarithm (ln) of both sides to eliminate the exponential term:
ln(0.1 / N₀) = -k * 5600
Now, we can solve for the rate constant (k) by rearranging the equation:
k = -ln(0.1 / N₀) / 5600
Since the rate constant is typically expressed in units of 'per time' (e.g., per hour), we can convert the time from minutes to hours:
k = -ln(0.1 / N₀) / (5600 / 60) = -ln(0.1 / N₀) / 93.33
The calculated value of the rate constant (k) represents the speed at which the radioactive sample decays. It is important to note that the rate constant is specific to the particular radioactive substance and is independent of the initial amount (N₀) of the sample.
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A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .?
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A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .?.
A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A radioactive sample decays to 10% of its initial amount in 5600 minutes. Calculate the rate constant of this process in h * r ^ - 1 .?.
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