Chapter 17: Problem 60

Write a nuclear equation for the alpha decay of each nuclide. (a) Po-218 (b) Po-214 (c) Po-210 (d) Th-227

Short Answer

Expert verified

\(_{84}^{218}\text{Po} \rightarrow _2^4\text{He} + _{82}^{214}\text{Pb}\), \(_{84}^{214}\text{Po} \rightarrow _2^4\text{He} + _{82}^{210}\text{Pb}\), \(_{84}^{210}\text{Po} \rightarrow _2^4\text{He} + _{82}^{206}\text{Pb}\), \(_{90}^{227}\text{Th} \rightarrow _2^4\text{He} + _{88}^{223}\text{Rn}\)

Step by step solution

Understanding Alpha Decay

Alpha decay is a type of radioactive decay where an atomic nucleus emits an alpha particle. An alpha particle is essentially a helium-4 nucleus, which means it contains 2 protons and 2 neutrons. The atomic number decreases by 2 and the mass number decreases by 4.

Writing the Equation for Po-218

Polonium-218 (Po-218) will emit an alpha particle (He-4 nucleus) to become Lead-214 (Pb-214). Start by writing down the initial nuclide on the left side of the equation: \[ _{84}^{218}\text{Po} \rightarrow \_2^4\text{He} + ? \]Then, subtract the atomic number and mass number of the alpha particle from the original nuclide to find the resulting nuclide:\[ _{84-2}^{218-4}\text{Pb} \]This yields the final nuclear equation for Po-218 alpha decay:\[ _{84}^{218}\text{Po} \rightarrow _2^4\text{He} + _{82}^{214}\text{Pb} \]

Writing the Equation for Po-214

Similarly for Po-214: \[ _{84}^{214}\text{Po} \rightarrow _2^4\text{He} + _{82}^{210}\text{Pb} \]

Writing the Equation for Po-210

And for Po-210: \[ _{84}^{210}\text{Po} \rightarrow _2^4\text{He} + _{82}^{206}\text{Pb} \]

Writing the Equation for Th-227

For Th-227 the process is the same, but it becomes Radon-223 (Rn-223): \[ _{90}^{227}\text{Th} \rightarrow _2^4\text{He} + _{88}^{223}\text{Rn} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Radioactive Decay

Radioactive decay is a fundamental process by which an unstable atomic nucleus loses energy by emitting radiation. One of the most common types of radioactive decay is alpha decay, where the nucleus releases an alpha particle consisting of two protons and two neutrons, effectively the same as a helium-4 nucleus.

This process is spontaneous and results in the transformation of one chemical element into another. Key to understanding radioactive decay is recognizing that it is a random process at the level of single atoms, governed by a characteristic half-life, which is the time required for half of any given quantity of an isotope to decay.

Nuclear Equations

A nuclear equation represents the changes in an atomic nucleus during radioactive decay. The notation involves writing the initial nuclide on one side and the decay products on the other, including any emitted particles like alpha particles in alpha decay. One must ensure that both the atomic number (protons) and mass number (protons plus neutrons) are conserved in the process.

For example, when polonium-218 undergoes alpha decay, the nuclear equation is balanced by subtracting the mass and atomic numbers of the alpha particle from polonium-218, leading to the formation of lead-214.

Polonium Decay

Polonium decay follows the principle of alpha decay, which involves the emission of an alpha particle. Polonium has several isotopes that undergo this form of decay, including Po-218, Po-214, and Po-210. Each of these isotopes will eject an alpha particle, causing the atomic number to decrease by 2 and the mass number to decrease by 4, creating a new isotope of lead.

For instance, Po-210 will decay to form Pb-206, signifying that two protons and two neutrons have been emitted from the original polonium nucleus. These nuclear changes are captured correctly by writing balanced nuclear equations as demonstrated in the step-by-step solutions.

Thorium Decay

Similar to polonium, isotopes of thorium can also experience alpha decay. Thorium-227 is one such isotope which, upon decay, emits an alpha particle and transforms into radon-223.

The decay of thorium and the resulting nuclear equations are important in various fields, such as radiometric dating and nuclear medicine. The clear presentation of each step in writing the nuclear equation allows students to understand the atomic transformations that occur during the decay process and demonstrates the conservation of mass and atomic numbers.

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Write a nuclear equation for the alpha decay of each nuclide. (a) Po-218 (b) Po-214 (c) Po-210 (d) Th-227

Short Answer

Step by step solution

Understanding Alpha Decay

Writing the Equation for Po-218

Writing the Equation for Po-214

Writing the Equation for Po-210

Writing the Equation for Th-227

Key Concepts

Radioactive Decay

Nuclear Equations

Polonium Decay

Thorium Decay

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