Knowing The Concept Of Beta Decay

In nuclear physics, beta decay (β decay) is a type of radioactive decay in which beta particles (fast-energy electrons or positrons) are emitted from the nucleus, converting the original nuclide into its nuclide isobar. For example, the beta decay of neutrons converts them into protons through the emission of electrons with antineutrinos. 

Conversely, in so-called positron emissions, photons are converted to neutrons by the emission of positrons with neutrinos. Neither beta particles nor associated (antineutrinos) are present in the pre-beta decay nuclei, but they are produced during decay. This process results in a stable proton-to-neutron ratio with unstable atoms. The probability that a nuclide will decay due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form so-called core bands or valleys of stability.

Beta-decay is the result of a weak force characterized by a relatively long decay time. The nucleus is composed of up quarks and down quarks, and by the weak force, the quarks emit W bosons to change their flavour, forming electron/anti-electron neutrinos or positron/neutrino pairs. For example, a neutron composed of two down quarks and one up quark decays into a proton composed of one down quark and two up quarks.

What happens in a negative beta(β–) decay?

In β– decay, the weak interaction converts an atomic nucleus into a nucleus with an atomic number increased by one while emitting an electron (e–) and an electron antineutrino (νe-). β−decay generally occurs in neutron-rich nuclei.

AXZ → AX’Z+1 + e– + ve-

Where A and Z are the mass numbers and atomic numbers of the decaying nuclei, and X and X’ are the start and end elements, respectively.

What are the equations of beta decay?

For β– decay 

AXZ → AX’Z+1 + e– + ve-

Now, the Q value for this decay is

Q = [mN (AXZ) – mN (AX’Z+1) – me – m-ve] c2

Where mN (AXZ) Is the mass of the nucleus of the AXZ atoms, it is the mass of the electron, m-ve and is the electron antineutrino mass of. In other words, the total energy released is the mass energy of the first nucleus minus the mass energy of the last nucleus, electrons, and antineutrinos. The nucleus mass mN is related to the standard atomic mass m.

m(AXZ) c2 = mN (AXZ) c2 + Zmec2– i=1 ZBi

The total atomic weight is the mass of the nucleus plus the mass of the electrons minus the sum of all the electron binding energies i=1 Z Bi for the atom. Here, Bi is the energy required to remove the ith electron from an atom, or ion.

This equation is rearranged to find mN (AXZ), and mN (AX’Z+1) is found similar to each other. Substituting these nuclear masses into the Q-value equation, ignoring the difference between the near-zero antineutrino mass and the very small electron binding energy of the high-Z atom.

Q = [mN (AXZ) – mN (AX’Z+1)] c2

This energy is carried away as kinetic energy by the electron and antineutrino.

For β+ decay

AXZ → AX’Z-1 + e+ + ve

Which gives,

Q = [mN (AXZ) – mN (AX’Z-1) – me – mve] c2

in the above equation, the electron masses do not cancel each other, and so,

Q = [m (AXZ) – m(AX’Z-1) – 2me] c2

Now, this equation will only proceed when the Q value is positive.𝛽 decay can occur when the mass of atom AXZ exceeds that of AX’Z-1 by at least twice the mass of the electron.

Conclusion: 

Radioactivity was discovered in uranium by Antoine Henri Becquerel in 1896 and was subsequently observed by Marie and Pierre Curie in thorium and the new elements polonium and radium. In 1899, Ernest Rutherford divided radioactive radiation into two types, alpha and beta (now beta-minus), based on their ability to cause the invasion and ionization of objects. Alpha rays can be stopped with thin paper or aluminium, but beta rays can penetrate a few millimetres of aluminium. In 1900, Paul Ulrich identified an even more permeable type of radiation. This was called gamma rays, identifying Rutherford as a radically new type in 1903. Alpha, beta, and gamma are the first three Greek letters.