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Most nuclei are not stable. They will decay after some period of time. The half-life of a given nucleus, which is a measure of how long it takes for half of a given sample to decay, can range from $\mu$s to hundreds of thousands of years.

Nuclear decay reactions must satisfy a number of conservation laws, including the law of charge conservation. There are four principle modes by which a nucleus can decay; $\beta$ decay, electron capture, $\alpha$ emission, and fission. The three are distinguished by the type of particles the nucleus breaks into.

A $\beta$ decay is simply the decay of a nucleus through the emission of either an electron ($e^-$), which is called “$\beta$-minus decay”, or a positron ($e^+$), which is called “$\beta$-plus decay”. Electron capture, in which a nucleus captures an electron and thereby changes its nuclear identity, is in many ways the inverse of $\beta$ decay, with the exception that one does not observe the capture of positrons, as they do not stably exist in atomic electron clouds.

In $\alpha$ decay, a nucleus emits an $\alpha$ particle, which is the nucleus of a $\rm{^4He}$ atom. The $\alpha$ particle has an electric charge of $+2e$, where:

$$e = 1.602 \times 10^{-19}\text{ C}$$

…is the electronic charge.

In a fission reaction, a nucleus decays to a pair of relatively heavy nuclei. Oftentimes the daughter nuclei in these reactions are also radioactive, so that a long chain of nuclear decays is initiated by the first decay.

Two other particles that sometimes appear in nuclear decay reactions are the neutrino ($\nu$) and the anti-neutrino ($\bar{\nu}$). These are both electrically neutral and do not affect the balance of charge in a reaction.

In the scientific literature, nuclei are generally labeled by the notation:

$$\rm{^AX}$$

…where the symbol $\rm{X}$ denotes what chemical element the reactant is. It may be $\rm{C}$ (Carbon), or $\rm{Mo}$ (Molybdenum), or whatever element appears in the reaction. This identifies the number of protons the nucleus has. The symbol $\rm{A}$ tells you the total number of nucleons, protons plus neutrons, in the element. This tells you which isotope of a particular element the nucleus is. One can see from the periodic table shown below, for example, that since carbon has six protons, the nucleus $\rm ^{14}C$ is an isotope of carbon that has $8 = 14 - 6$ neutrons.

Consider the following five nuclear decay reactions. Three of these reactions are permitted by charge conservation, and two of them are forbidden:

$\rm{^{60}Co} \rightarrow \rm{^{60}Ni} + e^- + \bar{\nu}$

$\rm{^{175}Pt} \rightarrow \rm{^{171}Os} + \alpha$

$\rm{^{128}Cs} + e^- \rightarrow \rm{^{128}Ba } + \nu$

$\rm{^{230}Pa} \rightarrow \rm{^{230}Th }+ e^+ + \nu$

$\rm{^{252}Es} \rightarrow \rm{^{140}I} + \rm{^{108}Ru} + 4n$

Select the TWO reactions that are forbidden because they violate charge conservation.

A

$\rm{^{60}Co} \rightarrow \rm{^{60}Ni} + e^- + \bar{\nu}$

B

$\rm{^{175}Pt} \rightarrow \rm{^{171}Os} + \alpha$

C

$\rm{^{128}Cs} + e^- \rightarrow \rm{^{128}Ba } + \nu$

D

$\rm{^{230}Pa} \rightarrow \rm{^{230}Th }+ e^+ + \nu$

E

$\rm{^{252}Es} \rightarrow \rm{^{140}I} + \rm{^{108}Ru} + 4n$

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