Question

Write a balanced nuclear equation for each of the following processes: (a) Beta emission from ruthenium- \(106:{ }_{44}^{106} \mathrm{Ru} \longrightarrow{ }_{-1}^{0} \mathrm{e}+\) ? (b) Alpha emission from bismuth- \(189:{ }_{83}^{189} \mathrm{Bi} \longrightarrow{ }_{2}^{4} \mathrm{He}+\) ? (c) Electron capture by polonium-204: \({ }_{84}^{204} \mathrm{Po}+{ }_{-1}^{0} e \stackrel{?}{?}\)

Short answer

(a) \( {}_{44}^{106}\mathrm{Ru} \rightarrow {}_{-1}^{0}e + {}_{45}^{106}\mathrm{Rh} \); (b) \( {}_{83}^{189}\mathrm{Bi} \rightarrow {}_{2}^{4}He + {}_{81}^{185}Tl \); (c) \( {}_{84}^{204}\mathrm{Po} + {}_{-1}^{0}e \rightarrow {}_{83}^{204}Bi \)."

Step-by-step solution

Understand Beta Emission

Beta emission involves the release of a beta particle, which is essentially an electron, denoted as \( {}_{-1}^{0}e \). During this process, a neutron in the nucleus is converted into a proton, increasing the atomic number by one while the mass number remains unchanged.

Write the Balanced Equation for Beta Emission

Given \( {}_{44}^{106}\mathrm{Ru} \rightarrow {}_{-1}^{0}e + {}_{Z}^{106}Y \), increase the atomic number by 1. So, \( Z = 45 \) since the mass number remains 106. The product will be \( {}_{45}^{106}\mathrm{Rh} \). Thus, the balanced equation is: \( {}_{44}^{106}\mathrm{Ru} \rightarrow {}_{-1}^{0}e + {}_{45}^{106}\mathrm{Rh} \).

Understand Alpha Emission

Alpha emission involves the release of an alpha particle, denoted as \( {}_{2}^{4}He \). During this process, the atomic number decreases by 2 and the mass number decreases by 4.

Write the Balanced Equation for Alpha Emission

For \( {}_{83}^{189}\mathrm{Bi} \rightarrow {}_{2}^{4}He + {}_{81}^{185}X \), subtract 2 from the atomic number and 4 from the mass number. Thus, the product is \( {}_{81}^{185}Tl \). The balanced equation is: \( {}_{83}^{189}\mathrm{Bi} \rightarrow {}_{2}^{4}He + {}_{81}^{185}Tl \).

Understand Electron Capture

Electron capture involves capturing an inner orbital electron by the nucleus, leading to the conversion of a proton into a neutron. This decreases the atomic number by 1 while the mass number remains unchanged.

Write the Balanced Equation for Electron Capture

For \( {}_{84}^{204}\mathrm{Po} + {}_{-1}^{0}e \rightarrow {}_{83}^{204}X \), decrease the atomic number by 1 while keeping the mass number the same. The product is \( {}_{83}^{204}Bi \). The balanced equation is: \( {}_{84}^{204}\mathrm{Po} + {}_{-1}^{0}e \rightarrow {}_{83}^{204}Bi \).

Key concepts

Beta Emission

Beta emission is a type of radioactive decay where an unstable nucleus releases a beta particle. A beta particle is essentially an electron, denoted by the symbol \( {}_{-1}^{0}e \). But where does this electron come from? In beta emission, a neutron inside the nucleus is transformed into a proton. This process increases the atomic number by one, changing the identity of the element, while the mass number remains the same.
For example, consider the beta emission from ruthenium-106: \( {}_{44}^{106} ext{Ru} \rightarrow {}_{-1}^{0} ext{e} + {}_{45}^{106} ext{Rh} \). The neutron in the nucleus of ruthenium becomes a proton, making the resulting atom rhodium rather than ruthenium.
Beta emission is one of the ways elements can transform into different elements, and it plays a crucial role in the balance of protons and neutrons in unstable nuclei.

Alpha Emission

Alpha emission is another form of radioactive decay in which an unstable nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, akin to a helium nucleus, and is symbolized by \( {}_{2}^{4} ext{He} \). This process results in the loss of four units from the mass number and a reduction of the atomic number by two.
For instance, during the alpha emission of bismuth-189, the equation \( {}_{83}^{189} ext{Bi} \rightarrow {}_{2}^{4} ext{He} + {}_{81}^{185} ext{Tl} \) is balanced by reducing both the mass and atomic numbers correctly.
Alpha emission significantly alters the original atom, turning it into a completely different element. This kind of nuclear reaction is commonly observed in heavy elements and contributes significantly to nuclear stability adjustments.

Electron Capture

Electron capture is a unique process of nuclear decay where an electron from the innermost energy level (like the K-shell) is absorbed by the nucleus. This process converts a proton into a neutron, decreasing the atomic number by one while the mass number remains unchanged.
For example, in electron capture by polonium-204, the reaction \( {}_{84}^{204} ext{Po} + {}_{-1}^{0}e \rightarrow {}_{83}^{204} ext{Bi} \) results in the formation of bismuth. Here, the captured electron allows a proton to change into a neutron, effectively moving the element one place down in the periodic table from polonium to bismuth.
Electron capture is an important process that typically occurs in proton-rich nuclei, helping to achieve a stable isotopic configuration.