The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons. It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated (less than 0.1% difference for most nuclides) by its mass number, which indicates that most of the mass of a nucleus arises from mass of its constituent protons and neutrons. Thus, the mass excess is an expression of the nuclear binding energy, relative to the binding energy per nucleon of carbon-12 (which defines the dalton). If the mass excess is negative, the nucleus has more binding energy than 12C, and vice versa. If a nucleus has a large excess of mass compared to a nearby nuclear species, it can radioactively decay, releasing energy.
The 12C standard provides a convenient unit (the dalton) in which to express nuclear mass for defining the mass excess. However, its usefulness arises in the calculation of nuclear reaction kinematics or decay. Only a small fraction of the total energy that is associated with an atomic nucleus by mass–energy equivalence, on the order of 0.01% to 0.1% of the total mass, may be absorbed or liberated as radiation. By working in terms of the mass excess, much of the mass changes which arise from the transfer or release of nucleons is effectively removed, highlighting the net energy difference.
Nuclear reaction kinematics are customarily performed in units involving the electronvolt, which derives from accelerator technology. The combination of this practical point with the theoretical relation E = mc2 makes the unit megaelectronvolt over the speed of light squared (MeV/c2) a convenient form in which to express nuclear mass. However, the numerical values of nuclear masses in MeV/c2 are quite large (even the proton mass is ~938.27 MeV/c2), while mass excesses range in the tens of MeV/c2. This makes tabulated mass excess less cumbersome for use in calculations. The 1/c2 factor is typically omitted when quoting mass excess values in MeV, since the interest is more often energy and not mass; if one wanted units of mass, one would simply change the units from MeV to MeV/c2 without altering the numerical value.
Example
Consider the nuclear fission of 236U into 92Kr, 141Ba, and three neutrons.
236U → 92Kr + 141Ba + 3 n
The mass number of the reactant, 236U, is 236. Because the actual mass is 236.045563Da, its mass excess is +0.045563 Da. Calculated in the same manner, the respective mass excesses for the products, 92Kr, 141Ba, and three neutrons, are −0.073843 Da, −0.085588 Da and 3 × 0.008665 Da = +0.025994 Da, respectively, for a total mass excess of −0.133437 Da. The difference between the mass excess of the reactants and that of the products is 0.179000 Da, which shows that the mass excess of the products is less than that of the reactants, and so the fission can occur – a calculation which could have also been done with only the masses of the reactants.
The mass excess can be converted into energy using 1 Da = 931.494 MeV/c2, and E = mc2, yielding 166.737 MeV.
Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017). "The NUBASE2016 evaluation of nuclear properties" (PDF). Chinese Physics C. 41 (3): 030001. Bibcode:2017ChPhC..41c0001A. doi:10.1088/1674-1137/41/3/030001.
March 09, 2023
mass, excess, mass, excess, nuclide, difference, between, actual, mass, mass, number, daltons, predominant, methods, tabulating, nuclear, mass, mass, atomic, nucleus, well, approximated, less, than, difference, most, nuclides, mass, number, which, indicates, t. The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons It is one of the predominant methods for tabulating nuclear mass The mass of an atomic nucleus is well approximated less than 0 1 difference for most nuclides by its mass number which indicates that most of the mass of a nucleus arises from mass of its constituent protons and neutrons Thus the mass excess is an expression of the nuclear binding energy relative to the binding energy per nucleon of carbon 12 which defines the dalton If the mass excess is negative the nucleus has more binding energy than 12C and vice versa If a nucleus has a large excess of mass compared to a nearby nuclear species it can radioactively decay releasing energy Contents 1 Energy scale of nuclear reactions 2 Example 3 References 4 External linksEnergy scale of nuclear reactions EditThe 12C standard provides a convenient unit the dalton in which to express nuclear mass for defining the mass excess However its usefulness arises in the calculation of nuclear reaction kinematics or decay Only a small fraction of the total energy that is associated with an atomic nucleus by mass energy equivalence on the order of 0 01 to 0 1 of the total mass may be absorbed or liberated as radiation By working in terms of the mass excess much of the mass changes which arise from the transfer or release of nucleons is effectively removed highlighting the net energy difference Nuclear reaction kinematics are customarily performed in units involving the electronvolt which derives from accelerator technology The combination of this practical point with the theoretical relation E mc2 makes the unit megaelectronvolt over the speed of light squared MeV c2 a convenient form in which to express nuclear mass However the numerical values of nuclear masses in MeV c2 are quite large even the proton mass is 938 27 MeV c2 while mass excesses range in the tens of MeV c2 This makes tabulated mass excess less cumbersome for use in calculations The 1 c2 factor is typically omitted when quoting mass excess values in MeV since the interest is more often energy and not mass if one wanted units of mass one would simply change the units from MeV to MeV c2 without altering the numerical value Example EditConsider the nuclear fission of 236U into 92Kr 141Ba and three neutrons 236U 92Kr 141Ba 3 nThe mass number of the reactant 236U is 236 Because the actual mass is 236 045563 Da its mass excess is 0 045563 Da Calculated in the same manner the respective mass excesses for the products 92Kr 141Ba and three neutrons are 0 073843 Da 0 085588 Da and 3 0 008665 Da 0 025994 Da respectively for a total mass excess of 0 133437 Da The difference between the mass excess of the reactants and that of the products is 0 179000 Da which shows that the mass excess of the products is less than that of the reactants and so the fission can occur a calculation which could have also been done with only the masses of the reactants The mass excess can be converted into energy using 1 Da 931 494 MeV c2 and E mc2 yielding 166 737 MeV References EditKrane K S 1987 Introductory Nuclear Physics John Wiley amp Sons ISBN 0 471 80553 X Tipler P A Llewellyn R A 2004 Modern Physics W H Freeman and Company ISBN 0 7167 4345 0 External links EditAudi G Kondev F G Wang M Huang W J Naimi S 2017 The NUBASE2016 evaluation of nuclear properties PDF Chinese Physics C 41 3 030001 Bibcode 2017ChPhC 41c0001A doi 10 1088 1674 1137 41 3 030001 Retrieved from https en wikipedia org w index php title Mass excess amp oldid 1124618089, wikipedia, wiki, book, books, library,
