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

The accompanying graph illustrates the decay of ${ }_{42}^{88}$ Mo, which decays via positron emission. (a) What is the halflife of the decay? (b) What is the rate constant for the decay? (c) What fraction of the original sample of ${ }_{4}^{88}$ Mo remains after 12 minutes? (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 involves the transformation of one element into another and is governed by probabilistic laws that dictate how quickly a material will decay over time.

Half-life

The half-life is the time required for half of the radioactive material to decay. It is a key parameter that characterizes the decay process and is used to describe the rate at which unstable nuclei transform into their daughter products.

Decay Constant

The decay constant is a parameter that quantifies the probability per unit time that a nucleus will decay. It is directly related to the half-life by an inverse logarithmic relationship and is essential in determining the exponential decay behavior of radioactive substances.

Exponential Decay Law

The exponential decay law describes how the quantity of a radioactive substance decreases over time. It is mathematically modeled by an exponential function that incorporates the decay constant, allowing for the calculation of the fraction of a sample remaining after a given period.

Positron Emission

Positron emission is a type of radioactive decay where a proton in the nucleus is converted into a neutron, emitting a positron (the antimatter counterpart of the electron) and a neutrino. This process results in a decrease in the atomic number of the original element by one, yielding a new element as its decay product.

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