Question

Write balanced nuclear equations for the following processes: \((\mathbf{a})\) rubidium-90 undergoes beta emission; \((\mathbf{b})\) selenium- 72 undergoes electron capture; \((\mathbf{c})\) krypton-76 undergoes positron emission; \((\mathbf{d})\) radium-226 emits alpha radiation.

Short answer

The balanced nuclear equations for the given processes are: a) \( \mathrm{^{90}Rb} \rightarrow \mathrm{^{90}Sr} + \beta^{-} \) b) \( \mathrm{^{72}Se} + e^{-} \rightarrow \mathrm{^{72}As} \) c) \( \mathrm{^{76}Kr} \rightarrow \mathrm{^{76}Br} + \beta^{+} \) d) \( \mathrm{^{226}Ra} \rightarrow \mathrm{^{222}Rn} + \alpha \)

Step-by-step solution

Understanding the radioactive decay processes

To write balanced nuclear equations, we need to first understand the four radioactive decay processes: 1. Beta emission (β−): A neutron transforms into a proton, and an electron (beta particle) is emitted. 2. Electron capture (EC): A proton captures an electron and is transformed into a neutron. 3. Positron emission (β+): A proton transforms into a neutron, and a positron (antiparticle of an electron) is emitted. 4. Alpha radiation (α): An alpha particle (consisting of 2 protons and 2 neutrons) is emitted from the nucleus.

Writing balanced nuclear equations for each process

a) Rubidium-90 undergoes beta emission (β−): The atomic number of rubidium (Rb) is 37. During beta emission, a neutron transforms into a proton. Hence, the atomic number increases by 1. The mass number remains the same. \( \mathrm{^{90}Rb} \rightarrow \mathrm{^{90}Sr} + \beta^{-} \) b) Selenium-72 undergoes electron capture (EC): The atomic number of selenium (Se) is 34. During electron capture, a proton captures an electron and is transformed into a neutron. Hence, the atomic number decreases by 1. The mass number remains the same. \( \mathrm{^{72}Se} + e^{-} \rightarrow \mathrm{^{72}As} \) c) Krypton-76 undergoes positron emission (β+): The atomic number of krypton (Kr) is 36. During positron emission, a proton transforms into a neutron, and a positron is emitted. Hence, the atomic number decreases by 1. The mass number remains the same. \( \mathrm{^{76}Kr} \rightarrow \mathrm{^{76}Br} + \beta^{+} \) d) Radium-226 emits alpha radiation (α): The atomic number of radium (Ra) is 88. During alpha radiation, an alpha particle (consisting of 2 protons and 2 neutrons) is emitted. Hence, the atomic number decreases by 2, and the mass number decreases by 4. \( \mathrm{^{226}Ra} \rightarrow \mathrm{^{222}Rn} + \alpha \)

Key concepts

Beta Emission

In beta emission, an unstable atomic nucleus emits a beta particle, which is an electron or positron. When a neutron in the nucleus turns into a proton, an electron, otherwise known as a beta minus particle \(\beta^-\), is ejected. This phenomenon increases the atomic number by one while keeping the mass number unchanged.

For instance, in the beta emission of rubidium-90, the nuclear equation is \( ^{90}_{37}\text{Rb} \rightarrow ^{90}_{38}\text{Sr} + \beta^-\). The product is strontium-90, and the shift from rubidium to strontium occurs because the atomic number increases from 37 to 38 due to the extra proton formed during the decay process.

Understanding beta emission is fundamental in areas such as nuclear physics, medicine, and radioactive dating.

Electron Capture

Electron capture is a process where an inner orbital electron is captured by the nucleus and combines with a proton to form a neutron. This results in a decrease in the atomic number by one, but the mass number does not change.

In selenium-72 undergoing electron capture, the balanced nuclear equation is \( ^{72}_{34}\text{Se} + e^- \rightarrow ^{72}_{33}\text{As}\). This reaction shows that selenium is transformed into arsenic because the atomic number falls from 34 to 33 due to the conversion of a proton into a neutron.

This process has execution in nuclear medicine, such as in diagnostic procedures where certain isotopes used tend to decay by electron capture.

Positron Emission

Positron emission, also known as beta plus decay \(\beta^+\), occurs when a proton in an atomic nucleus is transformed into a neutron, and a positron is subsequently emitted. The atomic number decreases by one, yet the mass number remains the same.

If we look at the case of krypton-76, the nuclear equation for positron emission is \( ^{76}_{36}\text{Kr} \rightarrow ^{76}_{35}\text{Br} + \beta^+\). The nucleus of krypton becomes bromine, which has an atomic number one less than krypton since a proton is replaced by a neutron.

Positrons are antimatter counterparts to electrons and positron emission is utilized in medical imaging, specifically PET scans, which allow for the observation of metabolic processes in the body.

Alpha Radiation

Alpha radiation is a type of radioactive decay where an unstable nucleus emits an alpha particle, which consists of two protons and two neutrons (equivalent to a helium nucleus). This emission results in a decrease in both the atomic number and the mass number of the original atom.

For radium-226 emitting alpha radiation, the balanced nuclear equation is written as \( ^{226}_{88}\text{Ra} \rightarrow ^{222}_{86}\text{Rn} + \alpha\). When radium undergoes alpha decay, it changes into radon while losing two protons and two neutrons, leading to a lower atomic number (88 to 86) and mass number (from 226 to 222).

Alpha particles are relatively large and carry a double positive charge, which makes them interact intensely with matter. This characteristic makes alpha radiation significant in applications like smoke detectors and in treating certain types of cancer, where precision is necessary to avoid damaging adjacent healthy cells.