Consider the induced nuclear reaction 1^2 H+ 7^14 N → 6^12 C+ 2^4 He . The atomic masses are

step 1 Solving this problem, so first calculating M initial, which is equal to 2 .014102 plus 14 .00307

Consider the induced nuclear reaction 1^2 H+ 7^14 N → 6^12...

Consider the induced nuclear reaction ${ }_{1}^{2} \mathrm{H}+{ }_{7}^{14} \mathrm{~N} \rightarrow{ }_{6}^{12} \mathrm{C}+{ }_{2}^{4} \mathrm{He} .$ The atomic masses are ${ }_{1}^{2} \mathrm{H}(2.014102 \mathrm{u}),{ }_{7}^{14} \mathrm{~N}(14.003074 \mathrm{u}),{ }_{6}^{12} \mathrm{C}(12.000000 \mathrm{u}),$ and ${ }_{2}^{4} \mathrm{He}$ $(4.002603 \mathrm{u}) .$ Determine the energy (in $\mathrm{MeV}$ ) released when the ${ }_{6}^{12} \mathrm{C}$ and ${ }_{2}^{4} \mathrm{He}$ nuclei are formed in this manner.

Consider the induced nuclear reaction ${ }_{1}^{2} \mathrm{H}+{ }_{7}^{14} \mathrm{~N} \rightarrow{ }_{6}^{12} \mathrm{C}+{ }_{2}^{4} \mathrm{He} .$ The atomic
masses are ${ }_{1}^{2} \mathrm{H}(2.014102 \mathrm{u}),{ }_{7}^{14} \mathrm{~N}(14.003074 \mathrm{u}),{ }_{6}^{12} \mathrm{C}(12.000000 \mathrm{u}),$ and ${ }_{2}^{4} \mathrm{He}$
$(4.002603 \mathrm{u}) .$ Determine the energy (in $\mathrm{MeV}$ ) released when the ${ }_{6}^{12} \mathrm{C}$ and ${ }_{2}^{4} \mathrm{He}$ nuclei are formed in this manner.

Key Concepts

Mass Defect

Mass defect is the difference in mass between the reactants and the products in a nuclear reaction. This difference is a measure of the binding energy that holds the nucleus together, and it is directly related to the energy released or absorbed during the reaction by the mass-energy equivalence principle.

Mass-Energy Equivalence

Mass-energy equivalence is a fundamental principle described by Einstein’s equation E=mc², which indicates that mass can be converted into energy and vice versa. In nuclear reactions, a small loss (or gain) in mass results in a correspondingly large amount of energy due to the large value of the speed of light squared.

Atomic Mass Unit and Energy Conversion

The atomic mass unit (u) is defined in such a way that it can be converted to energy using a conversion factor (approximately 931.5 MeV per u). This conversion is crucial when calculating the energy released in nuclear reactions, as it allows mass differences measured in atomic mass units to be expressed in terms of energy.

Nuclear Reaction Energetics

Nuclear reaction energetics involves calculating the energy released or required during a nuclear transformation by comparing the total masses of the reactants and products. A decrease in total mass results in energy being released, while an increase in mass indicates the absorption of energy, making this concept essential in understanding and quantifying nuclear reactions.

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