Question

Write balanced equations for each of the processes described below. a. Chromium-51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture. b. Iodine-131, used to treat hyperactive thyroid glands, decays by producing a \(\beta\) particle. c. Phosphorus-32, which accumulates in the liver, decays by \(\beta\) -particle production.

Short answer

a. \(^{51}\text{Cr} + e^- \rightarrow ^{51}\text{V} + \nu_e \) b. \(^{131}\text{I} \rightarrow ^{131}\text{Xe} + e^- + \bar{\nu}_e\) c. \(^{32}\text{P} \rightarrow ^{32}\text{S} + e^- + \bar{\nu}_e\)

Step-by-step solution

a. Chromium-51 Electron Capture Decay

Chromium-51, denoted as \(^{51}\text{Cr}\), decays by electron capture. The process of electron capture involves the capture of an inner shell electron by the nucleus, leading to a reduction in the atomic number by one and the emission of an X-ray photon or a neutrino. For Chromium-51 (\(Z=24\), \(A=51\)), the electron capture process results in the formation of a new element with atomic number 23 and mass number 51. The balanced nuclear equation for the electron capture decay of Chromium-51 is: \[^{51}\text{Cr} + e^- \rightarrow ^{51}\text{V} + \nu_e \] Here, \(^{51}\text{V}\) is Vanadium-51, and \(\nu_e\) is the electron neutrino.

b. Iodine-131 \(\beta\) Decay

Iodine-131, denoted as \(^{131}\text{I}\), decays via \(\beta\) decay (also known as beta-minus decay), which involves the conversion of a neutron into a proton in the nucleus, emitting an electron (\(e^-\)) and an electron antineutrino (\(\bar{\nu}_e\)) in the process. For Iodine-131 (\(Z=53\), \(A=131\)), the \(\beta\) decay process results in the formation of a new element with atomic number 54 and mass number 131. The balanced nuclear equation for the \(\beta\) decay of Iodine-131 is: \[^{131}\text{I} \rightarrow ^{131}\text{Xe} + e^- + \bar{\nu}_e\] Here, \(^{131}\text{Xe}\) is Xenon-131.

c. Phosphorus-32 \(\beta\) Decay

Phosphorus-32, denoted as \(^{32}\text{P}\), also decays via \(\beta\) decay (beta-minus decay). Similar to Iodine-131, the process involves the conversion of a neutron into a proton in the nucleus, emitting an electron (\(e^-\)) and an electron antineutrino (\(\bar{\nu}_e\)). For Phosphorus-32 (\(Z=15\), \(A=32\)), the \(\beta\) decay process results in the formation of a new element with atomic number 16 and mass number 32. The balanced nuclear equation for the \(\beta\) decay of Phosphorus-32 is: \[^{32}\text{P} \rightarrow ^{32}\text{S} + e^- + \bar{\nu}_e\] Here, \(^{32}\text{S}\) is Sulfur-32.

Key concepts

Electron Capture

Electron capture is a process in which an atom's nucleus absorbs one of its own orbital electrons, specifically from the inner electron shells. This phenomenon occurs because the nucleus contains too many protons, making the atom unstable. When electron capture happens, a proton in the nucleus combines with the captured electron to form a neutron; consequently, the atomic number decreases by one while the mass number remains the same. This process is symbolized in nuclear equations where an electron (\( e^- \)) reacts with the nucleus (\( ^{A}_{Z}\text{X} \) for an element X with atomic number Z and mass number A), leading to a daughter element with a lower atomic number (\( ^{A}_{Z-1}\text{Y} \)). These reactions often emit a neutrino (\( u_e \)) to conserve energy, momentum, and angular momentum. For example, in medical applications, chromium-51 decays into vanadium-51 through electron capture and is used to help monitor blood flow in the spleen.

Beta Decay

Beta decay represents a class of radioactive decay processes in which a beta particle, which is an energetic electron (\( e^- \)) or positron (\( e^+ \)), is emitted from an atomic nucleus. There are two types of beta decay: beta-minus (\( \beta^- \)) decay where a neutron transforms into a proton, releasing an electron and an electron antineutrino (\( \bar{u}_e \)); and beta-plus (\( \beta^+ \)) decay where a proton turns into a neutron, emitting a positron and an electron neutrino (\( u_e \)). For instance, iodine-131, a commonly used medical isotope in the treatment of thyroid conditions, undergoes beta-minus decay to become xenon-131. Similarly, phosphorus-32 decays into sulfur-32, also via beta-minus decay. These processes result in a new element with an increased atomic number but the same mass number and are essential in many medical diagnostic and treatment procedures.

Nuclear Chemistry

Nuclear chemistry encompasses the study of changes in atomic nuclei, such as those that occur during radioactive decay or nuclear reactions. Understanding nuclear reactions involves looking at the balance of protons and neutrons in a nucleus to predict stability and types of decay or transformations that an unstable isotope might undergo. Elements that have unstable nuclei are termed radioisotopes and undergo radioactive decay to reach a more stable form. This field of chemistry is crucial for various applications, from the generation of electricity in nuclear power plants to the dating of archaeological artifacts through carbon-14 decay. Moreover, nuclear chemical principles are important in the field of medicine, both for diagnostic imaging and for treatment of diseases, such as in the case of isotopes decaying via electron capture or beta decay as seen in the given examples.

Radioisotope Applications

Radioisotopes are used extensively in various industries, including medicine, where they are applied in both the diagnosis and treatment of illnesses. Diagnostic applications involve using gamma-emitting isotopes in imaging techniques, such as PET (Positron Emission Tomography) scans, which allow doctors to observe the function of organs and tissues. Therapeutically, beta-emitting isotopes like iodine-131 are used in radiotherapy to treat conditions such as thyroid cancer, as the beta particles efficiently kill diseased cells. Agricultural applications utilize radioisotopes to improve food preservation and in genetic engineering to develop more resistant crops. In scientific research, they function as tracers in biochemical experiments to understand complex processes. Furthermore, in the field of archaeology, the dating of ancient artifacts and fossils using radioisotopes like carbon-14 provides invaluable information about the past. The vast range of radioisotope applications demonstrates their significant role in advancing science and improving human lives.