The accompanying graph illustrates the decay of 42^88 Mo which decays via positron emission. (a)

step 1 Chapter 21, question 6. The accompanying graph illustrates the decay of MO. This is 42 to 88. Th

The accompanying graph illustrates the decay of 42^88 Mo...

The accompanying graph illustrates the decay of $_{42}^{88} \mathrm{Mo}$ which decays via positron emission. (a) What is the half-life of the decay? (b) What is the rate constant for the decay?(c) What fraction of the original sample of $_{42}^{88} \mathrm{Mo}$ remains after 12 $\mathrm{min}$ ? (d) What is the product of the decay process? [Section 21.4$]$

Key Concepts

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This process occurs spontaneously and transforms the original nucleus into a different state, often a different element, by expelling particles or electromagnetic energy.

Half-Life

The half-life is the time required for half of the nuclei in a radioactive sample to decay. It is a characteristic property of a radioactive substance and is crucial for determining how quickly the substance diminishes in quantity over time.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a given nucleus will decay. It is directly related to the half-life by the relation ? = ln(2)/t½ and appears in the exponential decay law governing the process.

Exponential Decay Equation

The exponential decay equation, given by N(t) = N? exp(??t), mathematically describes how the number of radioactive nuclei decreases over time. It is used to calculate quantities such as the remaining fraction of a sample after a given period.

Positron Emission

Positron emission is a type of beta decay in which a proton in the nucleus is transformed into a neutron with the emission of a positron and a neutrino. This decay mode results in the transmutation of the original element into a new element with an atomic number reduced by one.

Nuclear Transmutation

Nuclear transmutation refers to the process in which an element is changed into a different element as a result of nuclear reactions, such as radioactive decay. In the context of decay processes like positron emission, it explains how the identity of the nuclide changes when a proton is converted into a neutron.

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