{"id":23,"date":"2017-11-14T13:47:05","date_gmt":"2017-11-14T18:47:05","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/back-matter\/fundamental-constants\/"},"modified":"2017-11-14T13:47:05","modified_gmt":"2017-11-14T18:47:05","slug":"fundamental-constants","status":"publish","type":"back-matter","link":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/back-matter\/fundamental-constants\/","title":{"raw":"Fundamental Constants","rendered":"Fundamental Constants"},"content":{"raw":"<table id=\"fs-id1171242154153\" summary=\"This table has 3 columns labeled quantity, symbol and value. Each row describes 1 quantity as follows: Atomic mass unit, u, 1.660538782 in parentheses 83 into 10 to the power minus 27 kg or 9.31494028 in parentheses 23 MeV by c squared; Avogadro&#x2019;s number, N subscript A, 6.02214179 in parentheses 30 into 10 to the power 23 particles per mole; Bohr magneton, mu subscript b equal to e h bar upon 2 m subscript e, 9.27400915 in parentheses 23 into 10 to the power minus 24 J by T; Bohr radius, a subscript 0 equal to h bar squared upon m subscript e e squared k subscript e, 5.2917720859 in parentheses 36 into 10 to the power minus 11 m; Boltzmann&#x2019;s constant, k subscript B equal to R by N subscript A, 1.3806504 in parentheses 24 into 10 to the power 23 J by K; Compton wavelength, lambda subscript C equal to h upon m subscript e c,  2.4263102175 in parentheses 33 into 10 to the power minus 12 m; Coulomb constant, k subscript e equal to 1 upon 4 pi epsilon subscript 0, 8.987551788 into 10 to the power 9 N m squared by C squared exact; Deuteron mass, m subscript d, 3.34358320 in parentheses 17 into 10 to the power minus 27 kg or 2.013553212724 in parentheses 78 u or 1875.612859 MeV by c squared; Electron mass, m subscript e, 9.10938215 in parentheses 45 into 10 to the power minus 31 kg or 5.4857990943 in parentheses 23 into 10 to the power minus 4 u or 0.510998910 in parentheses 13 MeV by c squared; Electron volt, eV, 1.602176487 in parentheses 40 into 10 to the power minus 19 J; Elementary charge, e, 1.602176487 in parentheses 40 into 10 to the power minus 19 C; Gas constant, R, 8.314472 in parentheses 15 J by mol K; Gravitational constant, G, 6.67428 in parentheses 67 into 10 to the power minus 11 N m squared by kg squared; Neutron mass, m subscript n, 1.674927211 in parentheses 84 into 10 to the power minus 27 kg or 1.00866491597 in parentheses 43 u or 939.565346 in parentheses 23 MeV by c squared; Nuclear magneton, mu subscript n equal to e h bar upon 2 m subscript p, 5.05078324 in parentheses 13 into 10 to the power minus 27 J by T; Permeability of free space, mu subscript 0, 4 pi into 10 to the power minus 7 T m by A exact; Permittivity of free space; epsilon 0 equal to 1 upon mu 0 c squared, 8,854187817 into 10 to the power minus 12 C squared by N m squared exact; Planck&#x2019;s constant, h or h bar equal to h by 2 pi, 6.62606896 in parentheses 33 into 10 to the power minus 34 J s or 1.054571628, in parentheses 53 into 10 to the power minus 34 J s; Proton mass m subscript p, 1.672621637 in parentheses 83 into 10 to the power minus 27 kg or 1.00727646677 in parentheses 10 u or 938.272013 in parentheses 23 MeV by c squared; Rydberg constant, R subscript H, 1.0973731568527 in parentheses 73 into 10 to the power 7 m to the power minus 1; Speed of light in vacuum, c, 2.99792458 into 10 to the power 8 m by s exact.\"><caption><span>Fundamental Constants<\/span><em>Note:<\/em> These constants are the values recommended in 2006 by CODATA, based on a least-squares adjustment of data from different measurements. The numbers in parentheses for the values represent the uncertainties of the last two digits.<\/caption><thead><tr valign=\"top\"><th>Quantity<\/th><th>Symbol<\/th><th>Value<\/th><\/tr><\/thead><tbody><tr valign=\"top\"><td>Atomic mass unit<\/td><td>u<\/td><td>[latex]\\begin{array}{c}1.660 538 782\\phantom{\\rule{0.2em}{0ex}}\\left(83\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 931.494 028\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Avogadro\u2019s number<\/td><td>[latex]{N}_{\\text{A}}[\/latex]<\/td><td>[latex]6.022 141 79\\phantom{\\rule{0.2em}{0ex}}\\left(30\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{23}\\phantom{\\rule{0.2em}{0ex}}\\text{particles\/mol}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Bohr magneton<\/td><td>[latex]{\\mu }_{\\text{B}}=\\frac{e\\hslash }{2{m}_{e}}[\/latex]<\/td><td>[latex]9.274 009 15\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-24}\\phantom{\\rule{0.2em}{0ex}}\\text{J\/T}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Bohr radius<\/td><td>[latex]{a}_{0}=\\frac{{\\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}[\/latex]<\/td><td>[latex]5.291 772 085 9\\phantom{\\rule{0.2em}{0ex}}\\left(36\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-11}\\phantom{\\rule{0.2em}{0ex}}\\text{m}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Boltzmann\u2019s constant<\/td><td>[latex]{k}_{\\text{B}}=\\frac{R}{{N}_{\\text{A}}}[\/latex]<\/td><td>[latex]1.380 650 4\\phantom{\\rule{0.2em}{0ex}}\\left(24\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-23}\\phantom{\\rule{0.2em}{0ex}}\\text{J\/K}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Compton wavelength<\/td><td>[latex]{\\lambda }_{\\text{C}}=\\frac{h}{{m}_{e}c}[\/latex]<\/td><td>[latex]2.426 310 217 5\\phantom{\\rule{0.2em}{0ex}}\\left(33\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-12}\\phantom{\\rule{0.2em}{0ex}}\\text{m}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Coulomb constant<\/td><td>[latex]{k}_{e}=\\frac{1}{4\\pi {\\text{\u03b5}}_{0}}[\/latex]<\/td><td>[latex]8.987 551 788...\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{9}\\phantom{\\rule{0.2em}{0ex}}\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/C}}^{2}\\left(\\text{exact}\\right)[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Deuteron mass<\/td><td>[latex]{m}_{d}[\/latex]<\/td><td>[latex]\\begin{array}{c}3.343 583 20\\phantom{\\rule{0.2em}{0ex}}\\left(17\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 2.013 553 212 724\\left(78\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 1875.612 859\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Electron mass<\/td><td>[latex]{m}_{e}[\/latex]<\/td><td>[latex]\\begin{array}{c}9.109 382 15\\phantom{\\rule{0.2em}{0ex}}\\left(45\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-31}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 5.485 799 094 3\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 0.510 998 910\\phantom{\\rule{0.2em}{0ex}}\\left(13\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Electron volt<\/td><td>eV<\/td><td>[latex]1.602 176 487\\phantom{\\rule{0.2em}{0ex}}\\left(40\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-19}\\phantom{\\rule{0.2em}{0ex}}\\text{J}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Elementary charge<\/td><td><em>e<\/em><\/td><td>[latex]1.602 176 487\\phantom{\\rule{0.2em}{0ex}}\\left(40\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-19}\\phantom{\\rule{0.2em}{0ex}}\\text{C}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Gas constant<\/td><td><em>R<\/em><\/td><td>[latex]8.314 472\\phantom{\\rule{0.2em}{0ex}}\\left(15\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{J\/mol}\u00b7\\text{K}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Gravitational constant\t<\/td><td><em>G<\/em><\/td><td>[latex]6.674 28\\phantom{\\rule{0.2em}{0ex}}\\left(67\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-11}\\phantom{\\rule{0.2em}{0ex}}\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/kg}}^{2}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Neutron mass<\/td><td>[latex]{m}_{n}[\/latex]<\/td><td>[latex]\\begin{array}{c}1.674 927 211\\phantom{\\rule{0.2em}{0ex}}\\left(84\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 1.008 664 915 97\\phantom{\\rule{0.2em}{0ex}}\\left(43\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 939.565 346\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Nuclear magneton<\/td><td>[latex]{\\mu }_{n}=\\frac{e\\hslash }{2{m}_{p}}[\/latex]<\/td><td>[latex]5.050 783 24\\phantom{\\rule{0.2em}{0ex}}\\left(13\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{J\/T}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Permeability of free space<\/td><td>[latex]{\\mu }_{0}[\/latex]<\/td><td>[latex]4\\pi \\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-7}\\phantom{\\rule{0.2em}{0ex}}\\text{T}\u00b7\\text{m\/A}\\left(\\text{exact}\\right)[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Permittivity of free space<\/td><td>[latex]{\\text{\u03b5}}_{0}=\\frac{1}{{\\mu }_{0}{c}^{2}}[\/latex]<\/td><td>[latex]8.854 187 817...\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-12}\\phantom{\\rule{0.2em}{0ex}}{\\text{C}}^{2}\\text{\/}\\text{N}\u00b7{\\text{m}}^{2}\\left(\\text{exact}\\right)[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Planck\u2019s constant<\/td><td><em>h<\/em><div><br \/><\/div>[latex]\\hslash =\\frac{h}{2\\pi }[\/latex]<\/td><td>[latex]\\begin{array}{c}6.626 068 96\\phantom{\\rule{0.2em}{0ex}}\\left(33\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-34}\\phantom{\\rule{0.2em}{0ex}}\\text{J}\u00b7\\text{s}\\hfill \\\\ 1.054 571 628\\phantom{\\rule{0.2em}{0ex}}\\left(53\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-34}\\phantom{\\rule{0.2em}{0ex}}\\text{J}\u00b7\\text{s}\\hfill \\end{array}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Proton mass<\/td><td>[latex]{m}_{p}[\/latex]<\/td><td>[latex]\\begin{array}{c}1.672 621 637\\phantom{\\rule{0.2em}{0ex}}\\left(83\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 1.007 276 466 77\\phantom{\\rule{0.2em}{0ex}}\\left(10\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 938.272 013\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Rydberg constant<\/td><td>[latex]{R}_{\\text{H}}[\/latex]<\/td><td>[latex]1.097 373 156 852 7\\phantom{\\rule{0.2em}{0ex}}\\left(73\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{7}\\phantom{\\rule{0.2em}{0ex}}{\\text{m}}^{-1}[\/latex]<\/td><\/tr><tr valign=\"top\"><td>Speed of light in vacuum<\/td><td><em>c<\/em><\/td><td>[latex]2.997 924 58\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{8}\\phantom{\\rule{0.2em}{0ex}}\\text{m\/s}\\phantom{\\rule{0.2em}{0ex}}\\left(\\text{exact}\\right)[\/latex]<\/td><\/tr><\/tbody><\/table><p id=\"fs-id1171242147204\"><strong>Useful combinations of constants for calculations:<\/strong><\/p><p id=\"fs-id1171242182102\">[latex]hc=12,400\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{\u00c5}=1240\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{nm}=1240\\phantom{\\rule{0.2em}{0ex}}\\text{MeV}\u00b7\\text{fm}[\/latex]<\/p><p id=\"fs-id1171242265876\">[latex]\\hslash c=1973\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{\u00c5}=197.3\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{nm}=197.3\\phantom{\\rule{0.2em}{0ex}}\\text{MeV}\u00b7\\text{fm}[\/latex]<\/p><p id=\"fs-id1171242091469\">[latex]{k}_{e}{e}^{2}=14.40\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{\u00c5}=1.440\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{nm}=1.440\\phantom{\\rule{0.2em}{0ex}}\\text{MeV}\u00b7\\text{fm}[\/latex]<\/p><p id=\"fs-id1171242324344\">[latex]{k}_{\\text{B}}T=0.02585\\phantom{\\rule{0.2em}{0ex}}\\text{eV at}\\phantom{\\rule{0.2em}{0ex}}T=300\\phantom{\\rule{0.2em}{0ex}}\\text{K}[\/latex]<\/p>","rendered":"<table id=\"fs-id1171242154153\" summary=\"This table has 3 columns labeled quantity, symbol and value. Each row describes 1 quantity as follows: Atomic mass unit, u, 1.660538782 in parentheses 83 into 10 to the power minus 27 kg or 9.31494028 in parentheses 23 MeV by c squared; Avogadro&#x2019;s number, N subscript A, 6.02214179 in parentheses 30 into 10 to the power 23 particles per mole; Bohr magneton, mu subscript b equal to e h bar upon 2 m subscript e, 9.27400915 in parentheses 23 into 10 to the power minus 24 J by T; Bohr radius, a subscript 0 equal to h bar squared upon m subscript e e squared k subscript e, 5.2917720859 in parentheses 36 into 10 to the power minus 11 m; Boltzmann&#x2019;s constant, k subscript B equal to R by N subscript A, 1.3806504 in parentheses 24 into 10 to the power 23 J by K; Compton wavelength, lambda subscript C equal to h upon m subscript e c,  2.4263102175 in parentheses 33 into 10 to the power minus 12 m; Coulomb constant, k subscript e equal to 1 upon 4 pi epsilon subscript 0, 8.987551788 into 10 to the power 9 N m squared by C squared exact; Deuteron mass, m subscript d, 3.34358320 in parentheses 17 into 10 to the power minus 27 kg or 2.013553212724 in parentheses 78 u or 1875.612859 MeV by c squared; Electron mass, m subscript e, 9.10938215 in parentheses 45 into 10 to the power minus 31 kg or 5.4857990943 in parentheses 23 into 10 to the power minus 4 u or 0.510998910 in parentheses 13 MeV by c squared; Electron volt, eV, 1.602176487 in parentheses 40 into 10 to the power minus 19 J; Elementary charge, e, 1.602176487 in parentheses 40 into 10 to the power minus 19 C; Gas constant, R, 8.314472 in parentheses 15 J by mol K; Gravitational constant, G, 6.67428 in parentheses 67 into 10 to the power minus 11 N m squared by kg squared; Neutron mass, m subscript n, 1.674927211 in parentheses 84 into 10 to the power minus 27 kg or 1.00866491597 in parentheses 43 u or 939.565346 in parentheses 23 MeV by c squared; Nuclear magneton, mu subscript n equal to e h bar upon 2 m subscript p, 5.05078324 in parentheses 13 into 10 to the power minus 27 J by T; Permeability of free space, mu subscript 0, 4 pi into 10 to the power minus 7 T m by A exact; Permittivity of free space; epsilon 0 equal to 1 upon mu 0 c squared, 8,854187817 into 10 to the power minus 12 C squared by N m squared exact; Planck&#x2019;s constant, h or h bar equal to h by 2 pi, 6.62606896 in parentheses 33 into 10 to the power minus 34 J s or 1.054571628, in parentheses 53 into 10 to the power minus 34 J s; Proton mass m subscript p, 1.672621637 in parentheses 83 into 10 to the power minus 27 kg or 1.00727646677 in parentheses 10 u or 938.272013 in parentheses 23 MeV by c squared; Rydberg constant, R subscript H, 1.0973731568527 in parentheses 73 into 10 to the power 7 m to the power minus 1; Speed of light in vacuum, c, 2.99792458 into 10 to the power 8 m by s exact.\">\n<caption><span>Fundamental Constants<\/span><em>Note:<\/em> These constants are the values recommended in 2006 by CODATA, based on a least-squares adjustment of data from different measurements. The numbers in parentheses for the values represent the uncertainties of the last two digits.<\/caption>\n<thead>\n<tr valign=\"top\">\n<th>Quantity<\/th>\n<th>Symbol<\/th>\n<th>Value<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Atomic mass unit<\/td>\n<td>u<\/td>\n<td>[latex]\\begin{array}{c}1.660 538 782\\phantom{\\rule{0.2em}{0ex}}\\left(83\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 931.494 028\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Avogadro\u2019s number<\/td>\n<td>[latex]{N}_{\\text{A}}[\/latex]<\/td>\n<td>[latex]6.022 141 79\\phantom{\\rule{0.2em}{0ex}}\\left(30\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{23}\\phantom{\\rule{0.2em}{0ex}}\\text{particles\/mol}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Bohr magneton<\/td>\n<td>[latex]{\\mu }_{\\text{B}}=\\frac{e\\hslash }{2{m}_{e}}[\/latex]<\/td>\n<td>[latex]9.274 009 15\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-24}\\phantom{\\rule{0.2em}{0ex}}\\text{J\/T}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Bohr radius<\/td>\n<td>[latex]{a}_{0}=\\frac{{\\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}[\/latex]<\/td>\n<td>[latex]5.291 772 085 9\\phantom{\\rule{0.2em}{0ex}}\\left(36\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-11}\\phantom{\\rule{0.2em}{0ex}}\\text{m}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Boltzmann\u2019s constant<\/td>\n<td>[latex]{k}_{\\text{B}}=\\frac{R}{{N}_{\\text{A}}}[\/latex]<\/td>\n<td>[latex]1.380 650 4\\phantom{\\rule{0.2em}{0ex}}\\left(24\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-23}\\phantom{\\rule{0.2em}{0ex}}\\text{J\/K}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Compton wavelength<\/td>\n<td>[latex]{\\lambda }_{\\text{C}}=\\frac{h}{{m}_{e}c}[\/latex]<\/td>\n<td>[latex]2.426 310 217 5\\phantom{\\rule{0.2em}{0ex}}\\left(33\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-12}\\phantom{\\rule{0.2em}{0ex}}\\text{m}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Coulomb constant<\/td>\n<td>[latex]{k}_{e}=\\frac{1}{4\\pi {\\text{\u03b5}}_{0}}[\/latex]<\/td>\n<td>[latex]8.987 551 788...\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{9}\\phantom{\\rule{0.2em}{0ex}}\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/C}}^{2}\\left(\\text{exact}\\right)[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Deuteron mass<\/td>\n<td>[latex]{m}_{d}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}3.343 583 20\\phantom{\\rule{0.2em}{0ex}}\\left(17\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 2.013 553 212 724\\left(78\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 1875.612 859\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Electron mass<\/td>\n<td>[latex]{m}_{e}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}9.109 382 15\\phantom{\\rule{0.2em}{0ex}}\\left(45\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-31}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 5.485 799 094 3\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-4}\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 0.510 998 910\\phantom{\\rule{0.2em}{0ex}}\\left(13\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Electron volt<\/td>\n<td>eV<\/td>\n<td>[latex]1.602 176 487\\phantom{\\rule{0.2em}{0ex}}\\left(40\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-19}\\phantom{\\rule{0.2em}{0ex}}\\text{J}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Elementary charge<\/td>\n<td><em>e<\/em><\/td>\n<td>[latex]1.602 176 487\\phantom{\\rule{0.2em}{0ex}}\\left(40\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-19}\\phantom{\\rule{0.2em}{0ex}}\\text{C}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Gas constant<\/td>\n<td><em>R<\/em><\/td>\n<td>[latex]8.314 472\\phantom{\\rule{0.2em}{0ex}}\\left(15\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{J\/mol}\u00b7\\text{K}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Gravitational constant\t<\/td>\n<td><em>G<\/em><\/td>\n<td>[latex]6.674 28\\phantom{\\rule{0.2em}{0ex}}\\left(67\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-11}\\phantom{\\rule{0.2em}{0ex}}\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/kg}}^{2}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Neutron mass<\/td>\n<td>[latex]{m}_{n}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}1.674 927 211\\phantom{\\rule{0.2em}{0ex}}\\left(84\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 1.008 664 915 97\\phantom{\\rule{0.2em}{0ex}}\\left(43\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 939.565 346\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Nuclear magneton<\/td>\n<td>[latex]{\\mu }_{n}=\\frac{e\\hslash }{2{m}_{p}}[\/latex]<\/td>\n<td>[latex]5.050 783 24\\phantom{\\rule{0.2em}{0ex}}\\left(13\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{J\/T}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Permeability of free space<\/td>\n<td>[latex]{\\mu }_{0}[\/latex]<\/td>\n<td>[latex]4\\pi \\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-7}\\phantom{\\rule{0.2em}{0ex}}\\text{T}\u00b7\\text{m\/A}\\left(\\text{exact}\\right)[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Permittivity of free space<\/td>\n<td>[latex]{\\text{\u03b5}}_{0}=\\frac{1}{{\\mu }_{0}{c}^{2}}[\/latex]<\/td>\n<td>[latex]8.854 187 817...\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-12}\\phantom{\\rule{0.2em}{0ex}}{\\text{C}}^{2}\\text{\/}\\text{N}\u00b7{\\text{m}}^{2}\\left(\\text{exact}\\right)[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Planck\u2019s constant<\/td>\n<td><em>h<\/em><\/p>\n<div><\/div>\n<p>[latex]\\hslash =\\frac{h}{2\\pi }[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}6.626 068 96\\phantom{\\rule{0.2em}{0ex}}\\left(33\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-34}\\phantom{\\rule{0.2em}{0ex}}\\text{J}\u00b7\\text{s}\\hfill \\\\ 1.054 571 628\\phantom{\\rule{0.2em}{0ex}}\\left(53\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-34}\\phantom{\\rule{0.2em}{0ex}}\\text{J}\u00b7\\text{s}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Proton mass<\/td>\n<td>[latex]{m}_{p}[\/latex]<\/td>\n<td>[latex]\\begin{array}{c}1.672 621 637\\phantom{\\rule{0.2em}{0ex}}\\left(83\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{-27}\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\hfill \\\\ 1.007 276 466 77\\phantom{\\rule{0.2em}{0ex}}\\left(10\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{u}\\hfill \\\\ 938.272 013\\phantom{\\rule{0.2em}{0ex}}\\left(23\\right)\\phantom{\\rule{0.2em}{0ex}}\\text{MeV\/}{c}^{2}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Rydberg constant<\/td>\n<td>[latex]{R}_{\\text{H}}[\/latex]<\/td>\n<td>[latex]1.097 373 156 852 7\\phantom{\\rule{0.2em}{0ex}}\\left(73\\right)\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{7}\\phantom{\\rule{0.2em}{0ex}}{\\text{m}}^{-1}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>Speed of light in vacuum<\/td>\n<td><em>c<\/em><\/td>\n<td>[latex]2.997 924 58\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}{10}^{8}\\phantom{\\rule{0.2em}{0ex}}\\text{m\/s}\\phantom{\\rule{0.2em}{0ex}}\\left(\\text{exact}\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171242147204\"><strong>Useful combinations of constants for calculations:<\/strong><\/p>\n<p id=\"fs-id1171242182102\">[latex]hc=12,400\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{\u00c5}=1240\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{nm}=1240\\phantom{\\rule{0.2em}{0ex}}\\text{MeV}\u00b7\\text{fm}[\/latex]<\/p>\n<p id=\"fs-id1171242265876\">[latex]\\hslash c=1973\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{\u00c5}=197.3\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{nm}=197.3\\phantom{\\rule{0.2em}{0ex}}\\text{MeV}\u00b7\\text{fm}[\/latex]<\/p>\n<p id=\"fs-id1171242091469\">[latex]{k}_{e}{e}^{2}=14.40\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{\u00c5}=1.440\\phantom{\\rule{0.2em}{0ex}}\\text{eV}\u00b7\\text{nm}=1.440\\phantom{\\rule{0.2em}{0ex}}\\text{MeV}\u00b7\\text{fm}[\/latex]<\/p>\n<p id=\"fs-id1171242324344\">[latex]{k}_{\\text{B}}T=0.02585\\phantom{\\rule{0.2em}{0ex}}\\text{eV at}\\phantom{\\rule{0.2em}{0ex}}T=300\\phantom{\\rule{0.2em}{0ex}}\\text{K}[\/latex]<\/p>\n","protected":false},"author":211,"menu_order":4,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"back-matter-type":[],"contributor":[],"license":[],"class_list":["post-23","back-matter","type-back-matter","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/pressbooks\/v2\/back-matter\/23","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":0,"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/pressbooks\/v2\/back-matter\/23\/revisions"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/pressbooks\/v2\/back-matter\/23\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/wp\/v2\/media?parent=23"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/pressbooks\/v2\/back-matter-type?post=23"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/wp\/v2\/contributor?post=23"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/universityphysicssandbox\/wp-json\/wp\/v2\/license?post=23"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}