{"id":1369,"date":"2018-02-26T20:35:44","date_gmt":"2018-02-26T20:35:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/?post_type=back-matter&p=1369"},"modified":"2018-02-26T20:35:44","modified_gmt":"2018-02-26T20:35:44","slug":"fundamental-constants","status":"publish","type":"back-matter","link":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/back-matter\/fundamental-constants\/","title":{"raw":"Fundamental Constants","rendered":"Fundamental Constants"},"content":{"raw":"
Fundamental Constants<\/span>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
Quantity<\/th>\nSymbol<\/th>\nValue<\/th>\n<\/tr><\/thead>
Atomic mass unit<\/td>\nu<\/td>\n$$\\begin{array}{c}1.660 538 782\\,(83)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 931.494 028\\,(23)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>
Avogadro\u2019s number<\/td>\n$${N}_{\\text{A}}$$<\/td>\n$$6.022 141 79\\,(30)\\,\u00d7\\,{10}^{23}\\,\\text{particles\/mol}$$<\/td>\n<\/tr>
Bohr magneton<\/td>\n$${\\mu }_{\\text{B}}=\\frac{e\\hslash }{2{m}_{e}}$$<\/td>\n$$9.274 009 15\\,(23)\\,\u00d7\\,{10}^{-24}\\,\\text{J\/T}$$<\/td>\n<\/tr>
Bohr radius<\/td>\n$${a}_{0}=\\frac{{\\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}$$<\/td>\n$$5.291 772 085 9\\,(36)\\,\u00d7\\,{10}^{-11}\\,\\text{m}$$<\/td>\n<\/tr>
Boltzmann\u2019s constant<\/td>\n$${k}_{\\text{B}}=\\frac{R}{{N}_{\\text{A}}}$$<\/td>\n$$1.380 650 4\\,(24)\\,\u00d7\\,{10}^{-23}\\,\\text{J\/K}$$<\/td>\n<\/tr>
Compton wavelength<\/td>\n$${\\lambda }_{\\text{C}}=\\frac{h}{{m}_{e}c}$$<\/td>\n$$2.426 310 217 5\\,(33)\\,\u00d7\\,{10}^{-12}\\,\\text{m}$$<\/td>\n<\/tr>
Coulomb constant<\/td>\n$${k}_{e}=\\frac{1}{4\\pi {\\text{\u03b5}}_{0}}$$<\/td>\n$$8.987 551 788...\\,\u00d7\\,{10}^{9}\\,\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/C}}^{2}(\\text{exact})$$<\/td>\n<\/tr>
Deuteron mass<\/td>\n$${m}_{d}$$<\/td>\n$$\\begin{array}{c}3.343 583 20\\,(17)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 2.013 553 212 724(78)\\,\\text{u}\\hfill \\\\ 1875.612 859\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>
Electron mass<\/td>\n$${m}_{e}$$<\/td>\n$$\\begin{array}{c}9.109 382 15\\,(45)\\,\u00d7\\,{10}^{-31}\\,\\text{kg}\\hfill \\\\ 5.485 799 094 3(23)\\,\u00d7\\,{10}^{-4}\\,\\text{u}\\hfill \\\\ 0.510 998 910\\,(13)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>
Electron volt<\/td>\neV<\/td>\n$$1.602 176 487\\,(40)\\,\u00d7\\,{10}^{-19}\\,\\text{J}$$<\/td>\n<\/tr>
Elementary charge<\/td>\ne<\/em><\/td>\n$$1.602 176 487\\,(40)\\,\u00d7\\,{10}^{-19}\\,\\text{C}$$<\/td>\n<\/tr>
Gas constant<\/td>\nR<\/em><\/td>\n$$8.314 472\\,(15)\\,\\text{J\/mol}\u00b7\\text{K}$$<\/td>\n<\/tr>
Gravitational constant\t<\/td>\nG<\/em><\/td>\n$$6.674 28\\,(67)\\,\u00d7\\,{10}^{-11}\\,\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/kg}}^{2}$$<\/td>\n<\/tr>
Neutron mass<\/td>\n$${m}_{n}$$<\/td>\n$$\\begin{array}{c}1.674 927 211\\,(84)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 1.008 664 915 97\\,(43)\\,\\text{u}\\hfill \\\\ 939.565 346\\,(23)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>
Nuclear magneton<\/td>\n$${\\mu }_{n}=\\frac{e\\hslash }{2{m}_{p}}$$<\/td>\n$$5.050 783 24\\,(13)\\,\u00d7\\,{10}^{-27}\\,\\text{J\/T}$$<\/td>\n<\/tr>
Permeability of free space<\/td>\n$${\\mu }_{0}$$<\/td>\n$$4\\pi \\,\u00d7\\,{10}^{-7}\\,\\text{T}\u00b7\\text{m\/A}(\\text{exact})$$<\/td>\n<\/tr>
Permittivity of free space<\/td>\n$${\\text{\u03b5}}_{0}=\\frac{1}{{\\mu }_{0}{c}^{2}}$$<\/td>\n$$8.854 187 817...\\,\u00d7\\,{10}^{-12}\\,{\\text{C}}^{2}\\text{\/}\\text{N}\u00b7{\\text{m}}^{2}(\\text{exact})$$<\/td>\n<\/tr>
Planck\u2019s constant<\/td>\nh<\/em>\n\n$$\\hslash =\\frac{h}{2\\pi }$$<\/td>\n$$\\begin{array}{c}6.626 068 96\\,(33)\\,\u00d7\\,{10}^{-34}\\,\\text{J}\u00b7\\text{s}\\hfill \\\\ 1.054 571 628\\,(53)\\,\u00d7\\,{10}^{-34}\\,\\text{J}\u00b7\\text{s}\\hfill \\end{array}$$<\/td>\n<\/tr>
Proton mass<\/td>\n$${m}_{p}$$<\/td>\n$$\\begin{array}{c}1.672 621 637\\,(83)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 1.007 276 466 77\\,(10)\\,\\text{u}\\hfill \\\\ 938.272 013\\,(23)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>
Rydberg constant<\/td>\n$${R}_{\\text{H}}$$<\/td>\n$$1.097 373 156 852 7\\,(73)\\,\u00d7\\,{10}^{7}\\,{\\text{m}}^{-1}$$<\/td>\n<\/tr>
Speed of light in vacuum<\/td>\nc<\/em><\/td>\n$$2.997 924 58\\,\u00d7\\,{10}^{8}\\,\\text{m\/s}\\,(\\text{exact})$$<\/td>\n<\/tr><\/tbody><\/table>

Useful combinations of constants for calculations:<\/strong><\/p>\n

$$hc=12,400\\,\\text{eV}\u00b7\\text{\u00c5}=1240\\,\\text{eV}\u00b7\\text{nm}=1240\\,\\text{MeV}\u00b7\\text{fm}$$<\/p>\n

$$\\hslash c=1973\\,\\text{eV}\u00b7\\text{\u00c5}=197.3\\,\\text{eV}\u00b7\\text{nm}=197.3\\,\\text{MeV}\u00b7\\text{fm}$$<\/p>\n

$${k}_{e}{e}^{2}=14.40\\,\\text{eV}\u00b7\\text{\u00c5}=1.440\\,\\text{eV}\u00b7\\text{nm}=1.440\\,\\text{MeV}\u00b7\\text{fm}$$<\/p>\n

$${k}_{\\text{B}}T=0.02585\\,\\text{eV at}\\,T=300\\,\\text{K}$$<\/p>","rendered":"\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Fundamental Constants<\/span>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
Quantity<\/th>\nSymbol<\/th>\nValue<\/th>\n<\/tr>\n<\/thead>\n
Atomic mass unit<\/td>\nu<\/td>\n$$\\begin{array}{c}1.660 538 782\\,(83)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 931.494 028\\,(23)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>\n
Avogadro\u2019s number<\/td>\n$${N}_{\\text{A}}$$<\/td>\n$$6.022 141 79\\,(30)\\,\u00d7\\,{10}^{23}\\,\\text{particles\/mol}$$<\/td>\n<\/tr>\n
Bohr magneton<\/td>\n$${\\mu }_{\\text{B}}=\\frac{e\\hslash }{2{m}_{e}}$$<\/td>\n$$9.274 009 15\\,(23)\\,\u00d7\\,{10}^{-24}\\,\\text{J\/T}$$<\/td>\n<\/tr>\n
Bohr radius<\/td>\n$${a}_{0}=\\frac{{\\hslash }^{2}}{{m}_{e}{e}^{2}{k}_{e}}$$<\/td>\n$$5.291 772 085 9\\,(36)\\,\u00d7\\,{10}^{-11}\\,\\text{m}$$<\/td>\n<\/tr>\n
Boltzmann\u2019s constant<\/td>\n$${k}_{\\text{B}}=\\frac{R}{{N}_{\\text{A}}}$$<\/td>\n$$1.380 650 4\\,(24)\\,\u00d7\\,{10}^{-23}\\,\\text{J\/K}$$<\/td>\n<\/tr>\n
Compton wavelength<\/td>\n$${\\lambda }_{\\text{C}}=\\frac{h}{{m}_{e}c}$$<\/td>\n$$2.426 310 217 5\\,(33)\\,\u00d7\\,{10}^{-12}\\,\\text{m}$$<\/td>\n<\/tr>\n
Coulomb constant<\/td>\n$${k}_{e}=\\frac{1}{4\\pi {\\text{\u03b5}}_{0}}$$<\/td>\n$$8.987 551 788…\\,\u00d7\\,{10}^{9}\\,\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/C}}^{2}(\\text{exact})$$<\/td>\n<\/tr>\n
Deuteron mass<\/td>\n$${m}_{d}$$<\/td>\n$$\\begin{array}{c}3.343 583 20\\,(17)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 2.013 553 212 724(78)\\,\\text{u}\\hfill \\\\ 1875.612 859\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>\n
Electron mass<\/td>\n$${m}_{e}$$<\/td>\n$$\\begin{array}{c}9.109 382 15\\,(45)\\,\u00d7\\,{10}^{-31}\\,\\text{kg}\\hfill \\\\ 5.485 799 094 3(23)\\,\u00d7\\,{10}^{-4}\\,\\text{u}\\hfill \\\\ 0.510 998 910\\,(13)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>\n
Electron volt<\/td>\neV<\/td>\n$$1.602 176 487\\,(40)\\,\u00d7\\,{10}^{-19}\\,\\text{J}$$<\/td>\n<\/tr>\n
Elementary charge<\/td>\ne<\/em><\/td>\n$$1.602 176 487\\,(40)\\,\u00d7\\,{10}^{-19}\\,\\text{C}$$<\/td>\n<\/tr>\n
Gas constant<\/td>\nR<\/em><\/td>\n$$8.314 472\\,(15)\\,\\text{J\/mol}\u00b7\\text{K}$$<\/td>\n<\/tr>\n
Gravitational constant\t<\/td>\nG<\/em><\/td>\n$$6.674 28\\,(67)\\,\u00d7\\,{10}^{-11}\\,\\text{N}\u00b7{\\text{m}}^{2}{\\text{\/kg}}^{2}$$<\/td>\n<\/tr>\n
Neutron mass<\/td>\n$${m}_{n}$$<\/td>\n$$\\begin{array}{c}1.674 927 211\\,(84)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 1.008 664 915 97\\,(43)\\,\\text{u}\\hfill \\\\ 939.565 346\\,(23)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>\n
Nuclear magneton<\/td>\n$${\\mu }_{n}=\\frac{e\\hslash }{2{m}_{p}}$$<\/td>\n$$5.050 783 24\\,(13)\\,\u00d7\\,{10}^{-27}\\,\\text{J\/T}$$<\/td>\n<\/tr>\n
Permeability of free space<\/td>\n$${\\mu }_{0}$$<\/td>\n$$4\\pi \\,\u00d7\\,{10}^{-7}\\,\\text{T}\u00b7\\text{m\/A}(\\text{exact})$$<\/td>\n<\/tr>\n
Permittivity of free space<\/td>\n$${\\text{\u03b5}}_{0}=\\frac{1}{{\\mu }_{0}{c}^{2}}$$<\/td>\n$$8.854 187 817…\\,\u00d7\\,{10}^{-12}\\,{\\text{C}}^{2}\\text{\/}\\text{N}\u00b7{\\text{m}}^{2}(\\text{exact})$$<\/td>\n<\/tr>\n
Planck\u2019s constant<\/td>\nh<\/em><\/p>\n

$$\\hslash =\\frac{h}{2\\pi }$$<\/td>\n

$$\\begin{array}{c}6.626 068 96\\,(33)\\,\u00d7\\,{10}^{-34}\\,\\text{J}\u00b7\\text{s}\\hfill \\\\ 1.054 571 628\\,(53)\\,\u00d7\\,{10}^{-34}\\,\\text{J}\u00b7\\text{s}\\hfill \\end{array}$$<\/td>\n<\/tr>\n
Proton mass<\/td>\n$${m}_{p}$$<\/td>\n$$\\begin{array}{c}1.672 621 637\\,(83)\\,\u00d7\\,{10}^{-27}\\,\\text{kg}\\hfill \\\\ 1.007 276 466 77\\,(10)\\,\\text{u}\\hfill \\\\ 938.272 013\\,(23)\\,\\text{MeV\/}{c}^{2}\\hfill \\end{array}$$<\/td>\n<\/tr>\n
Rydberg constant<\/td>\n$${R}_{\\text{H}}$$<\/td>\n$$1.097 373 156 852 7\\,(73)\\,\u00d7\\,{10}^{7}\\,{\\text{m}}^{-1}$$<\/td>\n<\/tr>\n
Speed of light in vacuum<\/td>\nc<\/em><\/td>\n$$2.997 924 58\\,\u00d7\\,{10}^{8}\\,\\text{m\/s}\\,(\\text{exact})$$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Useful combinations of constants for calculations:<\/strong><\/p>\n

$$hc=12,400\\,\\text{eV}\u00b7\\text{\u00c5}=1240\\,\\text{eV}\u00b7\\text{nm}=1240\\,\\text{MeV}\u00b7\\text{fm}$$<\/p>\n

$$\\hslash c=1973\\,\\text{eV}\u00b7\\text{\u00c5}=197.3\\,\\text{eV}\u00b7\\text{nm}=197.3\\,\\text{MeV}\u00b7\\text{fm}$$<\/p>\n

$${k}_{e}{e}^{2}=14.40\\,\\text{eV}\u00b7\\text{\u00c5}=1.440\\,\\text{eV}\u00b7\\text{nm}=1.440\\,\\text{MeV}\u00b7\\text{fm}$$<\/p>\n

$${k}_{\\text{B}}T=0.02585\\,\\text{eV at}\\,T=300\\,\\text{K}$$<\/p>\n\n\t\t\t

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