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Questions and Answers
A process following first-order kinetics will always produce a constant intensity of radiation.
A process following first-order kinetics will always produce a constant intensity of radiation.
False
The rate of decay of a substance is inversely proportional to the intensity of radiation it produces.
The rate of decay of a substance is inversely proportional to the intensity of radiation it produces.
False
The amount of a substance is directly proportional to the rate of decay of the substance.
The amount of a substance is directly proportional to the rate of decay of the substance.
False
The rate of decay of a substance is directly proportional to the intensity of radiation it produces.
The rate of decay of a substance is directly proportional to the intensity of radiation it produces.
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The intensity of radiation produced by a substance is directly proportional to the square of the amount of the substance.
The intensity of radiation produced by a substance is directly proportional to the square of the amount of the substance.
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What is the value of 𝑁(0) given in the problem?
What is the value of 𝑁(0) given in the problem?
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What is the relationship between 𝑑𝑁(𝑡) and 𝑡?
What is the relationship between 𝑑𝑁(𝑡) and 𝑡?
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What is the value of 𝜆 given in the problem?
What is the value of 𝜆 given in the problem?
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What is the rate of decay of the substance at t=0?
What is the rate of decay of the substance at t=0?
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What is the amount of the substance at t=1?
What is the amount of the substance at t=1?
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What is the relationship between 𝑁(𝑡) and 𝑡?
What is the relationship between 𝑁(𝑡) and 𝑡?
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Study Notes
Radioactive Decay
- The intensity of radiation produced by a substance is directly proportional to the rate of decay and the amount of the substance.
- Radioactive decay follows first-order kinetics.
- There are three principal modes of decay: alpha, beta, and gamma decays.
Characteristics of Radioactive Decay
- The probability of decay is a constant, characteristic of all radioactive decay.
- The rate of decay is constant in time and proportional to the number of nuclei.
Decay Constant and Equation
- The decay constant (λ) is the constant of proportionality.
- The differential equation that describes the situation is: 𝑑𝑁(𝑡) = -𝜆𝑁(𝑡)
- The equation for the number of nuclei at time t is: 𝑁(𝑡) = 𝑁(0)𝑒 −𝜆𝑡
Half-Life
- An isotope's half-life allows us to determine how long a sample of a useful isotope will be available, and how long a sample of an undesirable or dangerous isotope must be stored before it decays to a low-enough radiation level.
- The half-life is a measure of the time it takes for the material to decay to half of its initial amount.
Example Calculations
- At t=0, 𝑁(0) = 𝑁(0) = 10
- At t=1, 𝑁(1) = 8 = 10 ∗ 𝑒 −𝜆∗1
- The decay constant (λ) can be calculated from the equation: 𝑙𝑛 (0.8) = −𝜆
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Description
Test your knowledge of the three main types of radioactive decay: alpha, beta, and gamma decay. Learn about the principles and characteristics of each mode. This quiz is perfect for students learning about nuclear physics and radioactivity.
