Problem 64 - Chemistry The Molecular Nature of Matter

Question

Write the balanced nuclear equation for each of the following nuclear reactions: (a) electron capture by iron-55, (b) beta emission by potassium-42, (c) positron emission by ruthenium-93, (d) alpha emission by californium- 251 .

Step-by-Step Solution

Answer

\(^{55}_{26}Fe + e^- \rightarrow ^{55}_{25}Mn + u_e\), \(^{42}_{19}K \rightarrow ^{42}_{20}Ca + e^- + \bar{u}_e\), \(^{93}_{44}Ru \rightarrow ^{93}_{43}Tc + e^+ + u_e\), \(^{251}_{98}Cf \rightarrow ^{247}_{96}Cm + ^{4}_{2}He\).

Step 1: Understanding Electron Capture

Electron capture is a process in which an inner shell electron combines with a proton in the nucleus to form a neutron and emit an electron neutrino. The atomic number decreases by one, but the mass number remains the same. In Iron-55, this can be represented as \(e^- + ^{55}_{26}Fe \rightarrow ^{55}_{25}Mn + u_e\).

Step 2: Writing the Beta Emission Equation

Beta emission means a neutron in the nucleus is converted to a proton and emits a beta particle (electron) and an antineutrino. The atomic number increases by one while the mass number remains constant. For Potassium-42, the equation is \(^{42}_{19}K \rightarrow ^{42}_{20}Ca + e^- + \bar{u}_e\).

Step 3: Describing Positron Emission

Positron emission occurs when a proton is transformed into a neutron with the emission of a positron and a neutrino. The atomic number decreases by one, but the mass number remains unchanged. The equation for Ruthenium-93 is \(^{93}_{44}Ru \rightarrow ^{93}_{43}Tc + e^+ + u_e\).

Step 4: Alpha Emission Representation

Alpha emission involves the release of an alpha particle from the nucleus, which contains two protons and two neutrons, reducing the atomic number by two and the mass number by four. Californium-251 undergoes alpha emission as follows: \(^{251}_{98}Cf \rightarrow ^{247}_{96}Cm + ^{4}_{2}He\), where \(^{4}_{2}He\) represents the alpha particle.

Key Concepts

Understanding Electron Capture

Electron capture is a fascinating process that occurs inside an atom's nucleus. Atomic nuclei are made of protons and neutrons, with protons being positively charged and neutrons electrically neutral. Sometimes, an atom's nucleus captures one of its own electrons, typically from the innermost shell.

This captured electron combines with a proton to produce a neutron and a neutrino, a nearly massless particle. What's spectacular about electron capture is that it causes the atom to transform into a different element because the number of protons, which determines the element's identity, decreases by one. However, the mass number, which is the total number of protons and neutrons, doesn't change.

For example, in the electron capture by iron-55, one electron (\(e^-\)) is captured by the nucleus (\(^{55}_{26}Fe\)), resulting in a manganese-55 atom (\(^{55}_{25}Mn\)) and the emission of an electron neutrino (\(u_e\)).

Beta Emission in Nuclei

Beta emission is another type of nuclear decay which plays a key role in the natural transmutation of elements. Unlike electron capture, beta emission increases the atomic number of an element by one, while keeping the mass number unchanged. This increase is due to the conversion of a neutron in the nucleus into a proton, which is accompanied by the release of a beta particle (which is an electron) and an antineutrino.

Consider potassium-42 (\(^{42}_{19}K\)). It emits a beta particle (\(e^-\)), along with an antineutrino (\(\bar{u}_e\)), resulting in calcium-42 (\(^{42}_{20}Ca\)). This process is a crucial part of many natural radioactive series and has applications in medical imaging and treatment, as well as carbon dating in archaeology.

Positron Emission and Isotopes

Positron emission is quite the opposite of beta emission. During positron emission, a proton inside the nucleus is transformed into a neutron and releases a positron (\(e^+\)), which is the antimatter counterpart of the electron, along with a neutrino. This nuclear reaction, again, leaves the mass number constant but lowers the atomic number by one, leading to the transformation into a new element.

For instance, ruthenium-93 (\(^{93}_{44}Ru\)) undergoes positron emission to become technetium-93 (\(^{93}_{43}Tc\)). Positron emission is not just a theoretical concept but is employed in positron emission tomography (PET), a cutting-edge medical imaging technique that helps detect diseases in the body.

Alpha Emission and Atomic Changes

Alpha emission is another way that unstable nuclei can reach a more stable state. An alpha particle, which consists of two protons and two neutrons bound together (\(^{4}_{2}He\)), is ejected from the nucleus. This emission results in the reduction of both atomic and mass numbers—by two and four, respectively. Alpha particles are relatively heavy and carry a double positive charge.

Californium-251 (\(^{251}_{98}Cf\) demonstrates alpha emission by releasing an alpha particle to form curium-247 (\(^{247}_{96}Cm\)). This process is crucial for understanding the synthesis and decay of heavy elements and is a common type of radiation in radioactive decay series seen in elements such as uranium and radium.