The carbon isotope ^15 C decays much faster than ^14 C. (a) Using Appendix B, write a nuclear

step 1 In this question, we are looking at the decay of carbon 15. And by looking at Appendix B the tab

The carbon isotope ^15 C decays much faster than ^14 C....

The carbon isotope ${ }^{15} \mathrm{C}$ decays much faster than ${ }^{14} \mathrm{C}$.
(a) Using Appendix B, write a nuclear reaction showing the decay of ${ }^{15} \mathrm{C}$. (b) How much energy is released when ${ }^{15} \mathrm{C}$ decays?

Key Concepts

Nuclear Reaction Equations

This concept involves writing chemical equations to represent the transformation of nuclei during a reaction. These equations detail the reactants and products, ensuring that conservation laws—such as conservation of nucleon number and charge—are upheld. They are essential in nuclear physics for clearly describing processes like radioactive decay.

Beta Decay

Beta decay is a type of radioactive decay in which a nucleus transforms by converting a neutron to a proton (or vice versa), accompanied by the emission of a beta particle (an electron or positron) and a neutrino or antineutrino. This process changes the atomic number while keeping the mass number approximately constant, and it is crucial for understanding the transformation of neutron-rich or proton-rich nuclei.

Q-value Calculation

The Q-value in nuclear reactions refers to the amount of energy released when a nucleus undergoes a reaction or decay. This energy is determined by the difference in mass between the initial and final particles of the reaction, with the excess mass converted into energy as described by fundamental physical laws.

Mass-Energy Equivalence

Mass-energy equivalence is articulated by Einstein's famous equation E = mc², highlighting that mass can be converted into energy and vice versa. In the context of nuclear reactions, even a small difference in mass between reactants and products can result in a significant amount of energy release, underscoring the principle behind the Q-value calculation.

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