What Is Mass Of Electron

Constant	Values	Units
grand e	9.109383 7015(28)×x−31 [i]	kg
	5.485799 090 65(16)×ten−iv [2]	Da
	0.510998 950 00(15)	MeV/c 2
m e c two	viii.187105 7769(25)×x−fourteen	J
	0.510998 950 00(15) [3]	MeV

The electron mass (symbol: yard _{due east} ) is the mass of a stationary electron, also known every bit the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about 9.109×10⁻³¹ kilograms or well-nigh five.486×10⁻⁴ daltons, which has an energy-equivalent of almost 8.187×ten⁻¹⁴ joules or about 0.511 MeV.^[iii]

Terminology [edit]

The term "rest mass" is sometimes used considering in special relativity the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated past voltages of over 100 kV.

For instance, the relativistic expression for the full energy, Due east, of an electron moving at speed ${\displaystyle 5}$ is

${\displaystyle E=\gamma m_{\text{e}}c^{2},}$

where the Lorentz factor is ${\displaystyle \gamma =ane/{\sqrt {1-v^{2}/c^{2}}}}$ . In this expression grand _e is the "rest mass", or more simply merely the "mass" of the electron. This quantity yard _e is frame invariant and velocity independent. However, some texts group the Lorentz cistron with the mass gene to ascertain a new quantity chosen the relativistic mass, m _relativistic = γm _e .

Decision [edit]

Since the electron mass determines a number of observed effects in atomic physics, there are potentially many ways to determine its mass from an experiment, if the values of other physical constants are already considered known.

Historically, the mass of the electron was determined directly from combining two measurements. The mass-to-charge ratio of the electron was offset estimated past Arthur Schuster in 1890 past measuring the deflection of "cathode rays" due to a known magnetic field in a cathode ray tube. Seven years later J. J. Thomson showed that cathode rays consist of streams of particles, to be chosen electrons, and made more precise measurements of their mass-to-charge ratio once again using a cathode ray tube.

The second measurement was of the charge of the electron. This was determined with a precision of amend than 1% by Robert A. Millikan in his oil drop experiment in 1909. Together with the mass-to-accuse ratio, the electron mass was determined with reasonable precision. The value of mass that was found for the electron was initially met with surprise by physicists, since it was then pocket-sized (less than 0.ane%) compared to the known mass of a hydrogen atom.

The electron rest mass can be calculated from the Rydberg constant R _∞ and the fine-structure abiding α obtained through spectroscopic measurements. Using the definition of the Rydberg constant:

${\displaystyle R_{\infty }={\frac {m_{\rm {e}}c\alpha ^{2}}{2h}},}$

thus

${\displaystyle m_{\rm {e}}={\frac {2R_{\infty }h}{c\alpha ^{2}}},}$

where c is the speed of light and h is the Planck constant.^[4] The relative doubt, 5×10^−eight in the 2006 CODATA recommended value,^[5] is due entirely to the uncertainty in the value of the Planck constant. With the re-definition of kilogram in 2019, there is no uncertainty by definition left in Planck constant anymore.

The electron relative diminutive mass can be measured directly in a Penning trap. It can likewise be inferred from the spectra of antiprotonic helium atoms (helium atoms where one of the electrons has been replaced by an antiproton) or from measurements of the electron g-factor in the hydrogenic ions ¹²C^five+ or ¹⁶O^seven+.

The electron relative diminutive mass is an adapted parameter in the CODATA ready of fundamental physical constants, while the electron rest mass in kilograms is calculated from the values of the Planck constant, the fine-construction constant and the Rydberg abiding, every bit detailed above.^{[4] [5]}

Relationship to other physical constants [edit]

The electron mass is used to calculate^{[ citation needed ]} the Avogadro constant N _A:

${\displaystyle N_{\rm {A}}={\frac {M_{\rm {u}}A_{\rm {r}}({\rm {e}})}{m_{\rm {e}}}}={\frac {M_{\rm {u}}A_{\rm {r}}({\rm {e}})c\alpha ^{2}}{2R_{\infty }h}}.}$

Hence it is also related to the atomic mass abiding g _u:

${\displaystyle m_{\rm {u}}={\frac {M_{\rm {u}}}{N_{\rm {A}}}}={\frac {m_{\rm {due east}}}{A_{\rm {r}}({\rm {east}})}}={\frac {2R_{\infty }h}{A_{\rm {r}}({\rm {e}})c\blastoff ^{2}}},}$

where Thou _u is the molar mass constant (divers in SI) and A _r(eastward) is a directly measured quantity, the relative atomic mass of the electron.

Note that m _u is divers in terms of A _r(e), and non the other manner circular, and and so the name "electron mass in atomic mass units" for A _r(e) involves a circular definition (at to the lowest degree in terms of practical measurements).

The electron relative diminutive mass also enters into the calculation of all other relative atomic masses. By convention, relative atomic masses are quoted for neutral atoms, but the actual measurements are fabricated on positive ions, either in a mass spectrometer or a Penning trap. Hence the mass of the electrons must be added back on to the measured values before tabulation. A correction must also be made for the mass equivalent of the bounden free energy E _b. Taking the simplest case of complete ionization of all electrons, for a nuclide X of atomic number Z,^[iv]

${\displaystyle A_{\rm {r}}({\rm {X}})=A_{\rm {r}}({\rm {X}}^{Z+})+ZA_{\rm {r}}({\rm {e}})-E_{\rm {b}}/m_{\rm {u}}c^{2}\,}$

As relative atomic masses are measured every bit ratios of masses, the corrections must be applied to both ions: the uncertainties in the corrections are negligible, as illustrated below for hydrogen ane and oxygen 16.

Physical parameter	oneH	16O
relative diminutive mass of the X Z+ ion	i.007276 466 77(10)	15.990528 174 45(18)
relative atomic mass of the Z electrons	0.000548 579 909 43(23)	0.004388 639 2754(xviii)
correction for the binding free energy	−0.000000 014 5985	−0.000002 194 1559
relative atomic mass of the neutral atom	i.007825 032 07(10)	15.994914 619 57(18)

The principle can be shown by the decision of the electron relative atomic mass by Farnham et al. at the University of Washington (1995).^[vi] It involves the measurement of the frequencies of the cyclotron radiation emitted by electrons and by ¹²C⁶⁺ ions in a Penning trap. The ratio of the 2 frequencies is equal to half dozen times the inverse ratio of the masses of the two particles (the heavier the particle, the lower the frequency of the cyclotron radiation; the higher the accuse on the particle, the higher the frequency):

${\displaystyle {\frac {\nu _{c}({}^{12}{\rm {C}}^{half dozen+})}{\nu _{c}({\rm {e}})}}={\frac {6A_{\rm {r}}({\rm {e}})}{A_{\rm {r}}({}^{12}{\rm {C}}^{6+})}}=0.000\,274\,365\,185\,89(58)}$

Equally the relative atomic mass of ¹²C^six+ ions is very most 12, the ratio of frequencies can be used to calculate a outset approximation to A _r(e), 5.486303 7178 ×ten⁻⁴ . This judge value is then used to calculate a first approximation to A _r(¹²C⁶⁺), knowing that Eastward _b(¹²C)/grand _u c ⁱⁱ (from the sum of the half-dozen ionization energies of carbon) is 1.1058674 ×10^{−half-dozen} : A _r(¹²C⁶⁺) ≈ eleven.996708 723 6367 . This value is then used to calculate a new approximation to A _r(e), and the process repeated until the values no longer vary (given the relative uncertainty of the measurement, two.one×10⁻⁹): this happens by the 4th cycle of iterations for these results, giving A _r(e) = five.485799 111(12)×10⁻⁴ for these data.

References [edit]

1. ^ "2018 CODATA Value: electron mass". The NIST Reference on Constants, Units, and Doubt. NIST. 20 May 2019. Retrieved 2019-05-20 .
2. ^ "2018 CODATA Value: electron mass in u". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-06-21 .
3. ^ ^{a b} "2018 CODATA Value: electron mass free energy equivalent in MeV". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2022-07-xi .
4. ^ ^{a b c} "CODATA Value: electron mass". The NIST Reference on Constants, Units and Uncertainty. May twenty, 2019. Retrieved May 20, 2019.
5. ^ ^{a b} The NIST reference on Constants, Units, and Incertitude, National Plant of Standards and Technology, x June 2009
6. ^ Farnham, D. Fifty.; Van Dyck Jr., R. S.; Schwinberg, P. B. (1995), "Determination of the Electron's Atomic Mass and the Proton/Electron Mass Ratio via Penning Trap Mass Spectroscopy", Phys. Rev. Lett., 75 (20): 3598–3601, Bibcode:1995PhRvL..75.3598F, doi:10.1103/PhysRevLett.75.3598, PMID 10059680

What Is Mass Of Electron,

Source: https://en.wikipedia.org/wiki/Electron_mass

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