Write the balanced nuclear equation for each of the following decays: (a) \(\alpha\) decay of californium-250; (b) positron decay of rubidium76 ; (c) electron capture by arsenic-73; (d) \(\beta^{-}\)decay of chromium- \(56 .\)

Alpha decay represents one of the types of natural radioactive processes by which unstable nuclei emit alpha particles to achieve more stable configurations. An alpha particle consists of two protons and two neutrons, which is effectively a helium nucleus represented as \textsuperscript{4}He. During alpha decay, the parent atom's mass number decreases by four, and the atomic number decreases by two.

For example, in the alpha decay of californium-250, the equation is written as: \[^{250}_{98}Cf \rightarrow ^{246}_{96}Cm + ^{4}_{2}He\]
After emitting an alpha particle, californium-250 transforms into curium-246 due to the loss of those two protons and two neutrons. This transmutation results in californium shifting two places back in the periodic table, as elements are arranged by their atomic numbers.

Positron emission, also known as \beta^+ decay, is another radioactive process, wherein a proton in the nucleus is converted into a neutron and a positron is emitted. Positrons are the antimatter counterparts to electrons, possessing the same mass as an electron but with a positive charge.

In the case of rubidium-76 undergoing positron decay, the balancing equation is: \[^{76}_{37}Rb \rightarrow ^{76}_{36}Kr + ^{0}_{+1}e\]
Here, the positron (\beta^+) carries away one positive charge, thus the atomic number decreases by one, resulting in the element krypton. The mass number remains unchanged as the process only involves the reconfiguration of subatomic particles within the nucleus.

Electron capture is a process where an inner atomic electron is drawn into the nucleus and combines with a proton to form a neutron and emit a neutrino. It's a type of decay that, like positron emission, results in the decrease of the atomic number by one while leaving the mass number unchanged.

For arsenic-73, the electron capture process is depicted as: \[^{73}_{33}As + ^{0}_{-1}e \rightarrow ^{73}_{32}Ge + u\]
Here, arsenic-73 absorbs an electron (^{0}_{-1}e), which leads to the production of germanium-73. The emitted neutrino (u) carries away energy, but since it has negligible mass, the mass number of the atom remains the same.

Beta minus (\beta^-) decay is a nuclear process in which a neutron is transformed into a proton, a beta particle (another name for an electron when emitted in this way), and an antineutrino. This type of decay results in an increase in atomic number by one since a new proton is added to the nucleus while the mass number remains constant.

Chromium-56 experiencing beta minus decay is represented as: \[^{56}_{24}Cr \rightarrow ^{56}_{25}Mn + ^{0}_{-1}e\]
The newly formed manganese-56 (^{56}_{25}Mn) includes one additional proton compared to the original chromium-56 nucleus, as indicated by the atomic number rising from 24 to 25. The emitted electron is signified by ^{0}_{-1}e, and this electron is what we refer to as a beta particle.