A229952 - OEIS

%I #41 Mar 22 2023 12:09:57

%S 2,7,3,0,9,2,4,2,9

%N Decimal expansion of m_e*c in SI units (kg*m/s), where m_e is the electron mass and c is the speed of light in vacuum.

%C The product m_e*c is also the denominator in the formula of the electron Compton wavelength: W_C = h/(m_e*c), where h is the Planck constant.

%C It appears that m_e*c is also the main constant in the formula of the relativistic momentum of the electron, if such formula is written as the product of a dimensionless factor and a constant with the same dimensions as the relativistic momentum. For instance, here we write p = [1/(c^2/v^2 - 1)^(1/2)]*m_e*c instead of the standard formula p = [1/(1 - v^2/c^2)^(1/2)]*m_e*v, where v is the speed of the electron. A trigonometric version of the formula is p = tan(x)*m_e*c hence tan(x) = p/(m_e*c) assuming that sin(x) = v/c and 0 < x < Pi/2. Also p = sinh(X)*m_e*c assuming that sin(x) = tanh(X) = v/c.

%C Also m_e*c is the main constant in the formula of the relativistic momentum of the electron, if such formula is written as p = [(E^2/E_0^2 - 1)^(1/2)]*m_e*c where E is the relativistic energy and E_0 is the energy at rest.

%C Also m_e*c is equivalent to the momentum of a photon whose energy is the same as the rest energy of an electron.

%C Also m_e*c is equivalent to the relativistic momentum of an electron whose velocity is equal to c/sqrt(2). For more information see A229962.

%F m_e*c = E_0/c = A081801 * A003678 = A081816 / A003678.

%e 2.73092429... * 10^-22 [kilogram * meter / second].

%Y Cf. A003676, A003678, A081801, A081816, A229962, A230436, A230844, A231350.

%K nonn,cons

%O -21,1

%A _Omar E. Pol_, Nov 12 2013