Problem 16 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

The isotope of \({ }_{90} \mathrm{Ra}^{231}\) can be converted to \({ }_{90} \mathrm{Th}^{227} \mathrm{by}\) (a) One alpha emission (b) Four beta emission (c) Two alpha and two beta emissions (d) One alpha and two beta emissions

Step-by-Step Solution

Answer

The isotope of Ra-231 can be converted to Th-227 by one alpha and two beta emissions (option D).

Step 1: Understanding Alpha Emission

Alpha emission is a type of radioactive decay in which an alpha particle, which consists of 2 protons and 2 neutrons (the equivalent of a helium-4 nucleus), is emitted from the parent nucleus. As a result, the mass number decreases by 4 and the atomic number decreases by 2.

Step 2: Understanding Beta Emission

Beta emission is another type of radioactive decay in which a beta particle is emitted. In beta-minus decay, a neutron is converted into a proton and a beta particle (an electron). The atomic number increases by 1, but the mass number remains the same.

Step 3: Option A: Assessing One Alpha Emission

For one alpha emission from Ra-231, the mass number would decrease by 4 to become 227 and the atomic number would decrease by 2 to become 88. This does not yield Th-227 with atomic number 90; hence, option A is incorrect.

Step 4: Option B: Assessing Four Beta Emissions

For four beta emissions, the mass number remains the same but the atomic number would increase by 4, resulting in an element with atomic number 94, which is not Th-227. Therefore, option B is incorrect.

Step 5: Option C: Assessing Two Alpha and Two Beta Emissions

Two alpha emissions would decrease the mass number by 8 (to 223) and the atomic number by 4 (to 86). Following that, two beta emissions would increase the atomic number back by 2 (to 88), but the mass number would remain 223. This process does not result in Th-227. Thus, option C is incorrect.

Step 6: Option D: Assessing One Alpha and Two Beta Emissions

One alpha emission would decrease the mass number by 4 (to 227) and the atomic number by 2 (to 88). Then, two beta emissions would increase the atomic number by 2 (back to 90) without changing the mass number. This process would result in Th-227, so option D is correct.

Key Concepts

Alpha Emission

Alpha emission is a fascinating phenomenon in the realm of nuclear chemistry. It's a type of radioactive decay where an unstable atom loses an alpha particle, which is essentially a helium-4 nucleus. This alpha particle is composed of 2 protons and 2 neutrons, making it quite hefty compared to other forms of radioactive emissions.

When an alpha particle is emitted, it's like the atom is shedding weight to become more stable. The mass number of the atom decreases by 4 (since that's the combined mass of the 2 protons and 2 neutrons), and the atomic number drops by 2 because it has lost 2 protons. Imagine you're in a hot air balloon tossing out sandbags to rise higher; that's what an atom does with alpha particles. Albeit, with a greater impact on its identity - it transforms into a new element entirely!

It's essential to understand this concept clearly, as alpha emission plays a crucial role in many nuclear chemistry problems. Students often encounter exercises where they must identify the resulting element after this type of decay, drastically altering both the mass and the atomic numbers.

Beta Emission

In beta emission, the change that occurs within an atom is like a complex dance of subatomic particles. There are two types of beta decay: beta-minus and beta-plus. In beta-minus decay, a neutron turns into a proton while releasing an electron (beta particle) and an antineutrino. This increases the atom's atomic number by 1 since protons define the identity of an element, but the mass number remains constant because a neutron has been replaced with a proton - they're nearly identical in mass.

On the other hand, beta-plus decay involves a proton being transformed into a neutron, a positron (the electron’s antimatter counterpart), and a neutrino. Interestingly, this process decreases the atomic number by 1. A neat trick to remember is this: beta-minus decay 'adds' a proton, while beta-plus decay 'subtracts' one. These transformations are at the heart of countless nuclear chemistry problems, requiring students to track atomic and mass numbers meticulously.

Studying beta emission can reveal how certain isotopes can morph into others, underpinning fundamental concepts in nuclear medicine, energy production, and radiometric dating. For students tackling textbook exercises on beta emission, understanding the nuance of how protons and neutrons interconvert is key to mastering the material.

Nuclear Chemistry Problems

Solving nuclear chemistry problems is a bit like being a detective, piecing together clues to understand the transformations that occur within an atom's nucleus. These problems often involve predicting the result of radioactive decay processes, such as alpha and beta emissions. The key to solving them is a clear understanding of the rules governing atomic stability and the changes in atomic and mass numbers during these emissions.

In exercises like the one involving \( _{90} \mathrm{Ra}^{231} \) and thorium (\( _{90} \mathrm{Th}^{227} \)), students must apply their knowledge of alpha and beta decay to find the path from one isotope to another. Tracking the changes in atomic and mass numbers for each emission type allows students to sketch a decay series that yields the correct end product. It's a careful process of elimination, reasoning, and sometimes, a bit of trial and error.

By methodically assessing each possible decay route, students learn not just to arrive at the correct answer, but also to understand why other paths don't fit the puzzle. These problem-solving skills are invaluable, extending beyond chemistry to many scientific and engineering disciplines. Clear, step-by-step thinking allows students to tackle even the most complex nuclear chemistry problems with confidence.