Question

Write nuclear equations to represent each of the following: a. alpha decay of Th-230 b. alpha decay of Po- 210 c. beta decay of Th-234 d. beta decay of \(\mathrm{Po}-218\)

Short answer

a. _{90}^{230}Th \rightarrow _{88}^{226}Ra + _{2}^{4}He, b. _{84}^{210}Po \rightarrow _{82}^{206}Pb + _{2}^{4}He, c. _{90}^{234}Th \rightarrow _{91}^{234}Pa + _{-1}^{0}e, d. _{84}^{218}Po \rightarrow _{85}^{218}At + _{-1}^{0}e

Step-by-step solution

Writing alpha decay equation for Th-230

Alpha decay involves the release of an alpha particle from the nucleus. An alpha particle consists of 2 protons and 2 neutrons, which is equivalent to a Helium nucleus, He^2+. The alpha decay of Thorium-230 (Th-230) can be represented by subtracting the alpha particle from the original nucleus. Use the conservation of mass and atomic numbers to find the resulting element.

Writing alpha decay equation for Po-210

Similarly to Step 1, write the alpha decay equation for Polonium-210 (Po-210) by subtracting an alpha particle from its nucleus. Again, conserve both mass and atomic numbers to ensure the equation is balanced and determine the resulting element.

Writing beta decay equation for Th-234

Beta decay involves the conversion of a neutron into a proton and an electron, where the electron (beta particle) is emitted. The atomic number increases by one, but the mass number remains the same. Write the beta decay equation for Thorium-234 (Th-234) by adding one to its atomic number to find the new element and balance the equation.

Writing beta decay equation for Po-218

Use the same process as in Step 3 to write the beta decay equation for Polonium-218 (Po-218). Increase the atomic number by one to find the resulting element and emit a beta particle, ensuring the mass number remains unchanged for the balance.

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay in which an unstable atomic nucleus releases an alpha particle and transforms into a lighter nucleus. An alpha particle is essentially a helium nucleus, which means it contains two protons and two neutrons. This is represented by the symbol 42He or 42\begin{align*}\textnormal{He}^2+.In writing a nuclear equation for alpha decay, the total mass and atomic numbers are conserved. This means that the sum of the mass and atomic number of the produced element and alpha particle equals those of the original unstable nucleus. For the alpha decay of Thorium-230, the reaction can be symbolically written as follows:\[_{90}^{230}\mathrm{Th} \to _{88}^{226}\mathrm{Ra} + _2^4\mathrm{He}\]Thorium-230 (Th-230) loses four units of mass and two units of atomic number, becoming Radon-226 (Ra-226) after emitting an alpha particle.

Beta Decay

Beta decay is another form of radioactive decay where a beta particle is emitted. This process occurs when a neutron in the nucleus of an atom is converted into a proton and an electron. The electron, called a beta particle (β-), is then ejected from the nucleus. During this transformation, the atomic number of the element increases by one, but the mass number remains constant since a proton is replaced with a neutron.
For Thorium-234's beta decay, the nuclear equation can be expressed as:\[_{90}^{234}\mathrm{Th} \to _{91}^{234}\mathrm{Pa} + \beta^- \]Here, the original atom Thorium-234 (Th-234) transforms into Protactinium-234 (Pa-234) and a beta particle is emitted. The atomic number increases by one, while the atomic mass remains unchanged, reflecting the conversion of a neutron to a proton in the atom's nucleus.

Thorium-230

Thorium-230 (Th-230) is a radioactive isotope and is part of the decay series that leads to the formation of lead-206. It undergoes alpha decay, which is a common decay mode for heavy nuclei such as those found in actinide elements.

Understanding the alpha decay of Thorium-230 is crucial for comprehending its role in the decay series, where it becomes a different element upon emission of an alpha particle. The decay process transforms Thorium-230 into Radon-226, a process that happens naturally over time and is important for dating rocks and minerals for geological and archeological purposes, using a technique known as uranium-lead dating.

Polonium-210

Polonium-210 (Po-210) is another radioactive isotope and is notorious for its high toxicity and for being a part of the natural decay chain of Uranium-238. Similar to Thorium-230, Polonium-210 also undergoes alpha decay, releasing an alpha particle to become a new, lighter element, in this case, Lead-206 (Pb-206).

The nuclear equation for this transformation appears as:\[_{84}^{210}\mathrm{Po} \to _{82}^{206}\mathrm{Pb} + _2^4\mathrm{He}\]Notably, Polonium-210 has applications in various fields, including antistatic devices and nuclear batteries, and it can also be found in tobacco smoke. Moreover, because of its intense radioactivity, it has also been used in nefarious practices, such as poisoning.