Problem 13 - Introductory Chemistry Atoms First

Question

Positron emission moves us one step to the left in the periodic table, and alpha emission moves us two steps to the left. Does this mean that, for a given parent isotope, the daughter isotope resulting from two successive positron emissions is the same as the daughter isotope resulting from one alpha emission?

Step-by-Step Solution

Answer

No, for a given parent isotope, the daughter isotope resulting from two successive positron emissions is not the same as the daughter isotope resulting from one alpha emission. After two positron emissions, the isotope becomes (Z-2, A), while after one alpha emission, the isotope becomes (Z-2, A-4). The atomic numbers are the same, but the mass numbers are different.

Step 1: Decay Definitions

Before proceeding, let's define the decay processes. - Positron emission: A positron is emitted when a proton in the nucleus transforms into a neutron. This results in a decrease in the atomic number (Z) by 1, leaving the mass number (A) unchanged. - Alpha emission: An alpha particle consists of 2 protons and 2 neutrons. During alpha emission, the nucleus loses an alpha particle, decreasing both the atomic number (Z) and the mass number (A) by 2 and 4, respectively.

Step 1: Two Positron Emissions

Suppose the parent isotope has atomic number Z and mass number A. After the first positron emission, the atomic number (Z) decreases by 1, but the mass number (A) remains the same. So, the isotope becomes (Z-1, A). After the second positron emission, the atomic number (Z) decreases by 1 once more. Therefore, the resulting isotope after two successive positron emissions becomes (Z-2, A).

Step 2: One Alpha Emission

For the same parent isotope with atomic number Z and mass number A, we will now consider the alpha emission case. During alpha emission, the atomic number (Z) decreases by 2, and the mass number (A) decreases by 4. So, the resulting isotope is (Z-2, A-4).

Step 3: Comparison

Now, we will compare the daughter isotopes from both cases to determine if they are the same or not. - Two successive positron emissions: (Z-2, A) - One alpha emission: (Z-2, A-4) The atomic numbers for both daughter isotopes are the same (Z-2) but the mass numbers are different (A and A-4). So, the daughter isotopes are not the same. Thus, for a given parent isotope, the daughter isotope resulting from two successive positron emissions is not the same as the daughter isotope resulting from one alpha emission.

Key Concepts

Positron Emission

Positron emission is a type of radioactive decay in which a proton inside an atomic nucleus is transformed into a neutron, and in the process, a positron (the antimatter counterpart of an electron) is emitted. This form of decay leads to a decrease in the atomic number (or the number of protons) of the element by 1. However, the mass number (the sum of protons and neutrons) remains unchanged because only a proton changes into a neutron without mass altering.

The primary outcome of positron emission is the formation of a new element that is positioned one step to the left on the periodic table from the parent isotope. This type of decay typically occurs in proton-rich nuclei, where an excess of protons exists compared to neutrons.

When examining nuclear decay processes, it is essential to understand that positron emission alters the element's identity but not its mass number. Here are some quick points to remember about positron emission:

• It decreases the atomic number by 1.
• The mass number stays the same.
• A new element is formed that is one spot to the left in the periodic table from the parent element.
• It is commonly found in the decay of isotopes with fewer neutrons than protons.

Alpha Emission

Alpha emission, also known as alpha decay, involves the release of an alpha particle from the nucleus of an atom. An alpha particle is essentially a helium nucleus, made up of 2 protons and 2 neutrons. This results in a substantial change to the nucleus's structure, decreasing the atomic number by 2 and the mass number by 4.

Alpha decay is characteristic of heavy nuclei in elements with a large number of protons and neutrons, such as uranium and radium. The loss of 4 nuclear particles during alpha emission results in a significant alteration, as the daughter isotope takes a position two steps to the left in the periodic table compared to the original element.

Understanding alpha emission is crucial for studies in nuclear chemistry and physics, as it illustrates how certain heavy elements evolve through radioactive decay and how energy is released in the process. To summarize alpha emission, remember these key points:

• The atomic number decreases by 2.
• The mass number decreases by 4.
• The resulting element is shifted two places left on the periodic table.
• It generally occurs in heavy nuclei with a surplus of nucleons.

Periodic Table

The periodic table is a systematic arrangement of the chemical elements, ordered by increasing atomic number, which is the number of protons in an atom's nucleus. This chart serves as a vital tool in chemistry by organizing elements according to patterns in their chemical properties and electron configurations.

The vertical columns of the periodic table are known as groups or families, and elements within a group share similar chemical behavior. The horizontal rows, known as periods, indicate elements with increasing atomic numbers. The configuration effectively predicts the types of atoms that will undergo nuclear decay processes, such as positron or alpha emission.

When atoms undergo transformation through nuclear decay, such as positron emission or alpha emission, their positions on the periodic table shift accordingly. Positron emission typically results in moving one step to the left, while alpha emission results in moving two steps to the left on the periodic table. These changes are dictated by alterations in the atomic number of the elements involved.

Here are some important topics related to the periodic table:

• Elements are listed in order by atomic number.
• Groups have similar properties and reactivity.
• Periods represent sequences of elements with increasing atomic numbers.
• Shifts on the periodic table occur with changes in the atomic number due to nuclear decay.