The nuclide ¹⁸F decays by both electron capture and β⁺ decay. Find the difference in the energy released by these two processes. The atomic masses are ¹⁸F = 18.000950 and ¹⁸O = 17.9991598.

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Identify the two decay processes: electron capture and beta-plus (β+) decay.

For electron capture, calculate the energy released using the mass difference between the parent nuclide (18F) and the daughter nuclide (18O).

For β+ decay, calculate the energy released by considering the mass difference between the parent nuclide (18F) and the daughter nuclide (18O), and account for the mass of the emitted positron.

Use the equation E = Δm * c^2 to convert the mass difference to energy, where Δm is the mass difference and c is the speed of light.

Find the difference in energy released between the two processes by subtracting the energy calculated for electron capture from the energy calculated for β+ decay.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Decay Processes

Nuclear decay processes, such as electron capture and beta-plus (β+) decay, involve the transformation of unstable nuclei into more stable forms. In electron capture, an electron is absorbed by a proton, converting it into a neutron and emitting a neutrino. In β+ decay, a proton is transformed into a neutron, emitting a positron and a neutrino. Understanding these processes is crucial for analyzing the energy changes associated with nuclear reactions.

Energy Release in Nuclear Reactions

The energy released during nuclear reactions is determined by the mass difference between the reactants and products, as described by Einstein's equation E=mc². When a nuclide undergoes decay, the mass of the resulting particles is often less than that of the original nuclide, and this mass defect is converted into energy. Calculating the energy released in different decay processes allows for a comparison of their efficiencies and impacts.

Atomic Mass and Mass Defect

Atomic mass is a measure of the mass of an atom, typically expressed in atomic mass units (amu). The mass defect refers to the difference between the total mass of the individual nucleons and the actual mass of the nucleus, which accounts for the binding energy that holds the nucleus together. In decay calculations, knowing the atomic masses of the involved nuclides is essential for determining the mass defect and, consequently, the energy released during the decay.