Beta Plus Decay

Functions
template<typename T >
T	EGXPhys::QValueBetaPlusDecayInMeV (const T massParentInu, const T massDaughterInu)
	Calculates the Q-value, \(Q\), of a beta plus, \(\beta^+\), decay nuclear reaction in megaelectron volts. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic. More...
template<typename T >
T	EGXPhys::QValueBetaPlusDecayInJ (const T massParentInu, const T massDaughterInu)
	Calculates the Q-value, \(Q\), of a beta plus, \(\beta^+\), decay nuclear reaction in joules. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic. More...
template<typename T >
T	EGXPhys::QValueDoubleBetaPlusDecayInMeV (const T massParentInu, const T massDaughterInu)
	Calculates the Q-value, \(Q\), of a double beta plus, \(\beta^+\), decay nuclear reaction in megaelectron volts. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic. More...
template<typename T >
T	EGXPhys::QValueDoubleBetaPlusDecayInJ (const T massParentInu, const T massDaughterInu)
	Calculates the Q-value, \(Q\), of a double beta plus, \(\beta^+\), decay nuclear reaction in joules. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic. More...

Detailed Description

Function Documentation

QValueBetaPlusDecayInJ()

template<typename T >

T EGXPhys::QValueBetaPlusDecayInJ	(	const T	massParentInu,
		const T	massDaughterInu
	)

Calculates the Q-value, \(Q\), of a beta plus, \(\beta^+\), decay nuclear reaction in joules. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic.

The Q-value, \(Q\), is the energy released during a nuclear reaction. The Q-value can be positive, negative or zero. For \(Q < 0\) the reaction is endothermic/endoergic resulting in the kinetic energy of the reaction being converted into mass or binding energy. For \(Q > 0\) the reaction is exothermic/exoergic resulting in the mass or binding energy being released as kinetic energy.

To calculate the Q-value it is the initial mass of the parent atom, \(m(\ce{ ^{A}_{Z}X_{N} })\), minus the final mass of the daughter atom, \(m(\ce{ ^{A}_{Z -1}Y_{N +1} })\), as well as the mass of a positron, \(m(\ce{ ^{0}_{+1}e_{0} })\). The mass of an electron, \(m(\ce{ ^{0}_{-1}e_{0} })\), is also subtracted to turn the ionized atom into a non-ionized one (which is typical for these calculations since ionized mass of atoms are rarely tabulated):

\[Q = \left ( m(\ce{ ^{A}_{Z}X_{N} })-m(\ce{ ^{A}_{Z -1}Y_{N +1} })-m(\ce{ ^{0}_{+1}e_{0} }) - m(\ce{ ^{0}_{-1}e_{0} }) \right) c^2\]

See http://www.nndc.bnl.gov/qcalc/ and http://www.nuclear-power.net/nuclear-power/nuclear-reactions/q-value-energetics-nuclear-reactions/ and https://en.wikipedia.org/wiki/Positron_emission

Equation taken from "Introductory Nuclear Physics" (Krane, 1987), p. 62 & p. 381

Parameters

massParentInu	\(m(\ce{ ^{A}_{Z}X_{N} })\ (u)\) Mass of parrent nucleus in unified atomic mass units.
massDaughterInu	\(m(\ce{ ^{A}_{Z -1}Y_{N +1} })\ (u)\) Mass of daughter nucleus in unified atomic mass units.

Returns

\(Q\ (J)\) Q-value. The energy in joules produced by a nuclear reaction.

See also

MassDefect() to calculate the mass defect of an atom.

NuclearBindingEnergy() to calculate binding energy, \(BE\), of an atom.

QValueAlphaDecayInJ() to calculate Q-Value for an alpha decay reaction in joules.

QValueBetaMinusDecayInJ() to calculate Q-Value for a beta minus decay reaction in joules.

QValueElectronCaptureInJ() to calculate Q-Value for a electron capture reaction in joules.

QValueNeutronEmissionInJ() to calculate Q-Value for an neutron emission reaction in joules.

QValueProtonEmissionInJ() to calculate Q-Value for a proton emission reaction in joules.

QValueBetaPlusDecayInMeV()

template<typename T >

T EGXPhys::QValueBetaPlusDecayInMeV	(	const T	massParentInu,
		const T	massDaughterInu
	)

Calculates the Q-value, \(Q\), of a beta plus, \(\beta^+\), decay nuclear reaction in megaelectron volts. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic.

The Q-value, \(Q\), is the energy released during a nuclear reaction. The Q-value can be positive, negative or zero. For \(Q < 0\) the reaction is endothermic/endoergic resulting in the kinetic energy of the reaction being converted into mass or binding energy. For \(Q > 0\) the reaction is exothermic/exoergic resulting in the mass or binding energy being released as kinetic energy.

To calculate the Q-value it is the initial mass of the parent atom, \(m(\ce{ ^{A}_{Z}X_{N} })\), minus the final mass of the daughter atom, \(m(\ce{ ^{A}_{Z -1}Y_{N +1} })\), as well as the mass of a positron, \(m(\ce{ ^{0}_{+1}e_{0} })\). The mass of an electron, \(m(\ce{ ^{0}_{-1}e_{0} })\), is also subtracted to turn the ionized atom into a non-ionized one (which is typical for these calculations since ionized mass of atoms are rarely tabulated):

\[Q = \left ( m(\ce{ ^{A}_{Z}X_{N} })-m(\ce{ ^{A}_{Z -1}Y_{N +1} })-m(\ce{ ^{0}_{+1}e_{0} }) - m(\ce{ ^{0}_{-1}e_{0} }) \right) c^2\]

See http://www.nndc.bnl.gov/qcalc/ and http://www.nuclear-power.net/nuclear-power/nuclear-reactions/q-value-energetics-nuclear-reactions/ and https://en.wikipedia.org/wiki/Positron_emission

Equation taken from "Introductory Nuclear Physics" (Krane, 1987), p. 62 & p. 381

Parameters

massParentInu	\(m(\ce{ ^{A}_{Z}X_{N} })\ (u)\) Mass of parrent nucleus in unified atomic mass units.
massDaughterInu	\(m(\ce{ ^{A}_{Z -1}Y_{N +1} })\ (u)\) Mass of daughter nucleus in unified atomic mass units.

Returns

\(Q\ (MeV)\) Q-value. The energy in megaelectron volts produced by a nuclear reaction.

See also

MassDefect() to calculate the mass defect of an atom.

NuclearBindingEnergy() to calculate binding energy, \(BE\), of an atom.

QValueAlphaDecayInMeV() to calculate Q-Value for an alpha decay reaction in megaelectron volts.

QValueBetaMinusDecayInMeV() to calculate Q-Value for a beta minus decay reaction in megaelectron volts.

QValueElectronCaptureInMeV() to calculate Q-Value for a electron capture reaction in megaelectron volts.

QValueNeutronEmissionInMeV() to calculate Q-Value for an neutron emission reaction in megaelectron volts.

QValueProtonEmissionInMeV() to calculate Q-Value for a proton emission reaction in megaelectron volts.

QValueDoubleBetaPlusDecayInJ()

template<typename T >

T EGXPhys::QValueDoubleBetaPlusDecayInJ	(	const T	massParentInu,
		const T	massDaughterInu
	)

Calculates the Q-value, \(Q\), of a double beta plus, \(\beta^+\), decay nuclear reaction in joules. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic.

The Q-value, \(Q\), is the energy released during a nuclear reaction. The Q-value can be positive, negative or zero. For \(Q < 0\) the reaction is endothermic/endoergic resulting in the kinetic energy of the reaction being converted into mass or binding energy. For \(Q > 0\) the reaction is exothermic/exoergic resulting in the mass or binding energy being released as kinetic energy.

To calculate the Q-value it is the initial mass of the parent atom, \(m(\ce{ ^{A}_{Z}X_{N} })\), minus the final mass of the daughter atom, \(m(\ce{ ^{A}_{Z -2}Y_{N +2} })\), as well as the mass of two positrons, \(m(\ce{ ^{0}_{+1}e_{0} })\). The mass two electrons, \(m(\ce{ ^{0}_{-1}e_{0} })\), are also subtracted to turn the ionized atom into a non-ionized one (which is typical for these calculations since ionized mass of atoms are rarely tabulated)::

\[Q = \left ( m(\ce{ ^{A}_{Z}X_{N} })-m(\ce{ ^{A}_{Z -2}Y_{N +2} })-2m(\ce{ ^{0}_{+2}e_{0} }) - 2m(\ce{ ^{0}_{-1}e_{0} }) \right) c^2\]

See http://www.nndc.bnl.gov/qcalc/ and http://www.nuclear-power.net/nuclear-power/nuclear-reactions/q-value-energetics-nuclear-reactions/ and https://en.wikipedia.org/wiki/Positron_emission

Equation taken from "Introductory Nuclear Physics" (Krane, 1987), p. 62 & p. 381

Parameters

massParentInu	\(m(\ce{ ^{A}_{Z}X_{N} })\ (u)\) Mass of parrent nucleus in unified atomic mass units.
massDaughterInu	\(m(\ce{ ^{A}_{Z -2}Y_{N +2} })\ (u)\) Mass of daughter nucleus in unified atomic mass units.

Returns

\(Q\ (J)\) Q-value. The energy in joules produced by a nuclear reaction.

See also

MassDefect() to calculate the mass defect of an atom.

NuclearBindingEnergy() to calculate binding energy, \(BE\), of an atom.

QValueAlphaDecayInJ() to calculate Q-Value for an alpha decay reaction in joules.

QValueBetaMinusDecayInJ() to calculate Q-Value for a beta minus decay reaction in joules.

QValueElectronCaptureInJ() to calculate Q-Value for a electron capture reaction in joules.

QValueNeutronEmissionInJ() to calculate Q-Value for an neutron emission reaction in joules.

QValueProtonEmissionInJ() to calculate Q-Value for a proton emission reaction in joules.

QValueDoubleBetaPlusDecayInMeV()

template<typename T >

T EGXPhys::QValueDoubleBetaPlusDecayInMeV	(	const T	massParentInu,
		const T	massDaughterInu
	)

Calculates the Q-value, \(Q\), of a double beta plus, \(\beta^+\), decay nuclear reaction in megaelectron volts. The Q-value allows you to determine if a nuclear reaction is endothermic or exothermic.

The Q-value, \(Q\), is the energy released during a nuclear reaction. The Q-value can be positive, negative or zero. For \(Q < 0\) the reaction is endothermic/endoergic resulting in the kinetic energy of the reaction being converted into mass or binding energy. For \(Q > 0\) the reaction is exothermic/exoergic resulting in the mass or binding energy being released as kinetic energy.

To calculate the Q-value it is the initial mass of the parent atom, \(m(\ce{ ^{A}_{Z}X_{N} })\), minus the final mass of the daughter atom, \(m(\ce{ ^{A}_{Z -2}Y_{N +2} })\), as well as the mass of two positrons, \(m(\ce{ ^{0}_{+1}e_{0} })\). The mass two electrons, \(m(\ce{ ^{0}_{-1}e_{0} })\), are also subtracted to turn the ionized atom into a non-ionized one (which is typical for these calculations since ionized mass of atoms are rarely tabulated)::

\[Q = \left ( m(\ce{ ^{A}_{Z}X_{N} })-m(\ce{ ^{A}_{Z -2}Y_{N +2} })-2m(\ce{ ^{0}_{+2}e_{0} }) - 2m(\ce{ ^{0}_{-1}e_{0} }) \right) c^2\]

See http://www.nndc.bnl.gov/qcalc/ and http://www.nuclear-power.net/nuclear-power/nuclear-reactions/q-value-energetics-nuclear-reactions/ and https://en.wikipedia.org/wiki/Positron_emission

Equation taken from "Introductory Nuclear Physics" (Krane, 1987), p. 62 & p. 381

Parameters

massParentInu	\(m(\ce{ ^{A}_{Z}X_{N} })\ (u)\) Mass of parrent nucleus in unified atomic mass units.
massDaughterInu	\(m(\ce{ ^{A}_{Z -2}Y_{N +2} })\ (u)\) Mass of daughter nucleus in unified atomic mass units.

Returns

\(Q\ (MeV)\) Q-value. The energy in megaelectron volts produced by a nuclear reaction.

See also

MassDefect() to calculate the mass defect of an atom.

NuclearBindingEnergy() to calculate binding energy, \(BE\), of an atom.

QValueAlphaDecayInMeV() to calculate Q-Value for an alpha decay reaction in megaelectron volts.

QValueBetaMinusDecayInMeV() to calculate Q-Value for a beta minus decay reaction in megaelectron volts.

QValueElectronCaptureInMeV() to calculate Q-Value for a electron capture reaction in megaelectron volts.

QValueNeutronEmissionInMeV() to calculate Q-Value for an neutron emission reaction in megaelectron volts.

QValueProtonEmissionInMeV() to calculate Q-Value for a proton emission reaction in megaelectron volts.