Question

Explain how simply examining the periodic table allows you to predict the daughter isotope in: (a) Alpha decay (b) Beta decay (c) Positron emission (d) Electron capture

Short answer

By examining the periodic table, you can predict the daughter isotopes in various radioactive decay processes as follows: (a) Alpha decay: The daughter isotope will have an atomic number 2 less than the parent isotope and mass number 4 less (Z-2, A-4). E.g., for \(^{238}U\), the daughter isotope is \(^{234}Th\). (b) Beta decay: The daughter isotope will have an atomic number 1 more than the parent isotope and the mass number remains unchanged (Z+1, A). E.g., for \(^{137}Cs\), the daughter isotope is \(^{137}Ba\). (c) Positron emission: The daughter isotope will have an atomic number 1 less than the parent isotope and the mass number remains unchanged (Z-1, A). E.g., for \(^{22}Na\), the daughter isotope is \(^{22}Ne\). (d) Electron capture: The daughter isotope will have an atomic number 1 less than the parent isotope and the mass number remains unchanged (Z-1, A). E.g., for \(^{207}Bi\), the daughter isotope is \(^{207}Pb\).

Step-by-step solution

Alpha decay definition and effect on atomic and mass numbers

In alpha decay, the parent isotope emits an alpha particle, which consists of 2 protons and 2 neutrons. Therefore, the daughter isotope will have an atomic number (Z) that is 2 less than the parent isotope and a mass number (A) that is 4 less than the parent isotope, written as Z-2 and A-4. #b)# Beta decay:

Beta decay definition and effect on atomic and mass numbers

In beta decay, one neutron in the parent isotope is converted into a proton, and an electron (called a beta particle) is emitted. The daughter isotope will have an atomic number (Z) that is 1 more than the parent isotope and the mass number (A) remains the same, written as Z+1 and A. #c)# Positron emission:

Positron emission definition and effect on atomic and mass numbers

In positron emission, one proton in the parent isotope is converted into a neutron, and a positron (the antimatter counterpart of an electron) is emitted. The daughter isotope will have an atomic number (Z) that is 1 less than the parent isotope and the mass number (A) remains the same, written as Z-1 and A. #d)# Electron capture:

Electron capture definition and effect on atomic and mass numbers

In electron capture, a proton in the parent isotope captures an electron (usually from the innermost electron shell) and is converted into a neutron. The daughter isotope will have an atomic number (Z) that is 1 less than the parent isotope and the mass number (A) remains the same, written as Z-1 and A. 2. Predict the daughter isotope based on the change in atomic and mass number. #a)# Alpha decay example

Predicting daughter isotope in alpha decay

Let's say the parent isotope is \(^{238}U\) (uranium-238), which has an atomic number of 92. During alpha decay, it will emit an alpha particle, leading to the formation of a daughter isotope with an atomic number of 92 - 2 = 90 and a mass number of 238 - 4 = 234. A quick examination of the periodic table reveals that the element with an atomic number of 90 is thorium (Th). Therefore, the daughter isotope produced will be \(^{234}Th\). #b)# Beta decay example

Predicting daughter isotope in beta decay

Let's say the parent isotopes is \(^{137}Cs\) (cesium-137), which has an atomic number of 55. During beta decay, one of its neutrons will convert to a proton and it will emit a beta particle. This will lead to a daughter isotope with an atomic number of 55+1 =56 and a mass number of 137 (remaining the same). Examining the periodic table reveals that the element with the atomic number of 56 is barium (Ba). Therefore, the daughter isotope produced will be \(^{137}Ba\). #c)# Positron emission example

Predicting daughter isotope in positron emission

Let's say the parent isotope is \(^{22}Na\) (sodium-22), which has an atomic number of 11. During positron emission, one of its protons will convert to a neutron and emit a positron. This leads to a daughter isotope with an atomic number of 11-1 = 10 and a mass number of 22 (remaining the same). A quick examination of the periodic table reveals that the element with an atomic number of 10 is neon (Ne). Therefore, the daughter isotope produced will be \(^{22}Ne\). #d)# Electron capture example

Predicting daughter isotope in electron capture

Let's say the parent isotope is \(^{207}Bi\) (bismuth-207), which has an atomic number of 83. During electron capture, one of its protons will capture an electron and convert to a neutron. This leads to a daughter isotope with an atomic number of 83-1 = 82 and a mass number of 207 (remaining the same). A quick examination of the periodic table reveals that the element with an atomic number of 82 is lead (Pb). Therefore, the daughter isotope produced will be \(^{207}Pb\).

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle to become more stable. An alpha particle consists of 2 protons and 2 neutrons, which is identical to a helium nucleus. When a parent isotope undergoes alpha decay, its atomic number decreases by 2, and its mass number decreases by 4. For example, if uranium-238 (\( ^{238}U \)) decays by emitting an alpha particle, the atomic number will change from 92 to 90, and the mass number will change from 238 to 234. This change results in the formation of thorium-234 (\( ^{234}Th \)), based on its position in the periodic table.

• Atomic number change: -2
• Mass number change: -4
• Example: \( ^{238}U \rightarrow ^{234}Th \)

Using the periodic table is key in predicting the new element formed after alpha decay, as each position correlates to a particular element.

Beta Decay

In beta decay, a neutron in an unstable nucleus is transformed into a proton, and a beta particle, which is essentially an electron, is emitted. This form of decay increases the atomic number by 1 while leaving the mass number unchanged. As an illustration, if cesium-137 (\( ^{137}Cs \)) undergoes beta decay, the atomic number increases from 55 to 56, while the mass number stays at 137. This transformation turns cesium into barium (\( ^{137}Ba \)).

• Atomic number change: +1
• Mass number change: 0
• Example: \( ^{137}Cs \rightarrow ^{137}Ba \)

By locating the resultant atomic number on the periodic table, one can easily identify the newly formed daughter isotope.

Positron Emission

Positron emission involves the transformation of a proton in a nucleus into a neutron, along with the emission of a positron. A positron is the antimatter equivalent of an electron. This type of decay decreases the atomic number by 1 while leaving the mass number unchanged. Take sodium-22 (\( ^{22}Na \)) as an example. As positron emission occurs, the atomic number decreases from 11 to 10, and the mass number remains at 22. This leads to the formation of neon-22 (\( ^{22}Ne \)).

• Atomic number change: -1
• Mass number change: 0
• Example: \( ^{22}Na \rightarrow ^{22}Ne \)

Evaluating the periodic table allows for straightforward identification of the element formed after positron emission.

Electron Capture

In electron capture, a proton in the nucleus captures an electron from the inner shell, resulting in the conversion of the proton into a neutron. This process reduces the atomic number by 1, and the mass number remains unchanged. For example, if bismuth-207 (\( ^{207}Bi \)) undergoes electron capture, the atomic number reduces from 83 to 82, and the mass number remains at 207. This transformation leads to the formation of lead-207 (\( ^{207}Pb \)).

• Atomic number change: -1
• Mass number change: 0
• Example: \( ^{207}Bi \rightarrow ^{207}Pb \)

By consulting the periodic table, it becomes easier to predict the new isotope formed via electron capture.