Question

Write balanced nuclear equations for the following processes: (a) Alpha emission of \({ }^{162} \mathrm{Re}\) (b) Electron capture of \({ }^{138} \mathrm{Sm}\) (c) Beta emission of \({ }^{18 s} \mathrm{~W}\) (d) Positron emission of \({ }^{165} \mathrm{Ta}\)

Short answer

(a) \( {}^{162}_{75} \text{Re} \rightarrow {}^{158}_{73} \text{Ta} + {}^{4}_{2} \text{He} \) (b) \( {}^{138}_{62} \text{Sm} + e^- \rightarrow {}^{138}_{61} \text{Pm} \) (c) \( {}^{185}_{74} \text{W} \rightarrow {}^{185}_{75} \text{Re} + {}^{0}_{-1} \text{e} \) (d) \( {}^{165}_{73} \text{Ta} \rightarrow {}^{165}_{72} \text{Hf} + {}^{0}_{+1} \text{e} \)

Step-by-step solution

Understanding Alpha Emission

In alpha emission, an alpha particle, which has the structure of a helium nucleus \( _2^4 \text{He} \), is emitted from the nucleus of an atom. This decreases the atomic number by 2 and the mass number by 4. Thus, the nuclear equation for the alpha emission of \( {}^{162}\text{Re} \) can be written as: \[ {}^{162}_{75} \text{Re} \rightarrow {}^{158}_{73} \text{Ta} + {}^{4}_{2} \text{He} \]

Understanding Electron Capture

In electron capture, an inner orbital electron is captured by the nucleus, which transforms a proton into a neutron, decreasing the atomic number by 1 but leaving the mass number unchanged. For \( {}^{138}\text{Sm} \), the reaction is: \[ {}^{138}_{62} \text{Sm} + e^- \rightarrow {}^{138}_{61} \text{Pm} \]

Understanding Beta Emission

Beta emission involves the transformation of a neutron into a proton, resulting in the emission of a beta particle \( _{-1}^0 \text{e} \) (an electron). This increases the atomic number by 1. For \( {}^{185}\text{W} \), the equation is: \[ {}^{185}_{74} \text{W} \rightarrow {}^{185}_{75} \text{Re} + {}^{0}_{-1} \text{e} \]

Understanding Positron Emission

In positron emission, a proton is transformed into a neutron, releasing a positron \( _{1}^0 \text{e} \). This decreases the atomic number by 1 while the mass number remains the same. Hence, for \( {}^{165}\text{Ta} \), the equation becomes: \[ {}^{165}_{73} \text{Ta} \rightarrow {}^{165}_{72} \text{Hf} + {}^{0}_{+1} \text{e} \]

Key concepts

Alpha Emission

Alpha emission is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons, similar to the nucleus of a helium atom, and is represented as \(_2^4 \text{He}\). During this process, the emitting atom loses two protons and two neutrons, resulting in a decrease in the atomic number by 2 and the mass number by 4. This transition leads the element to move two places down on the periodic table.

For example, when \(^{162}\mathrm{Re}\) undergoes alpha emission, it transforms into \(^{158}_{73} \mathrm{Ta}\), with the emission of an \(_2^4 \text{He}\) particle. The balanced nuclear equation for this transformation is:

\[ {}^{162}_{75} \text{Re} \rightarrow {}^{158}_{73} \text{Ta} + {}^{4}_{2} \text{He} \]

Key points about alpha emission:

• Decreases atomic number by 2
• Decreases mass number by 4
• Results in the creation of a new element that is different from the original element by its position on the periodic table

Beta Emission

Beta emission is a form of decay where a neutron in the nucleus is converted into a proton while emitting a beta particle, which is an electron \(_{-1}^0 \text{e}\). This process increases the atomic number by 1 since a neutron is replaced by a proton, but the mass number remains unchanged. Beta decay is responsible for increasing the atomic number of the element by transitioning to the next higher element in the periodic table.

Considering \(^{185}\mathrm{W}\), when it emits a beta particle, it is transformed into \(^{185}_{75} \mathrm{Re}\). The balanced equation for this conversion is:

\[ {}^{185}_{74} \text{W} \rightarrow {}^{185}_{75} \text{Re} + {}^{0}_{-1} \text{e} \]

Key points about beta emission:

• Increases atomic number by 1
• The mass number remains the same
• Leads the element to settle in the next position on the periodic table

Electron Capture

Electron capture is a process where the nucleus of an atom draws in one of its inner orbital electrons. This captured electron combines with a proton to form a neutron, effectively decreasing the atomic number by 1, while the mass number remains unchanged since the number of nucleons does not change.

An example is the electron capture by \(^{138}\mathrm{Sm}\), which results in \(^{138}_{61} \mathrm{Pm}\). The balanced nuclear reaction for this process is:

\[ {}^{138}_{62} \text{Sm} + e^- \rightarrow {}^{138}_{61} \text{Pm} \]

Key aspects of electron capture:

• Atomic number decreases by 1
• Mass number remains unchanged
• Involves transformation of a proton to a neutron within the nucleus

Positron Emission

Positron emission is a radioactive decay mode in which a proton inside a nucleus is converted into a neutron, releasing a positron \(_{1}^0 \text{e}\) in the process. This causes the atomic number to decrease by 1, while the mass number stays the same, because the change involves a transformation within nucleons.

For instance, in the positron emission by \(^{165}\mathrm{Ta}\), the resulting element is \(^{165}_{72} \mathrm{Hf}\), depicted by the equation:

\[ {}^{165}_{73} \text{Ta} \rightarrow {}^{165}_{72} \text{Hf} + {}^{0}_{+1} \text{e} \]

Important facts about positron emission:

• Decreases atomic number by 1
• Mass number remains unchanged
• Results in the conversion of a proton to a neutron
• Involves the emission of a particle with the same mass as an electron but with a positive charge