Problem 86 - A Complete Resource Book in Chemistry for JEE Main

Question

A sample of \({ }_{19} \mathrm{~K}^{40}\) contains invariably \({ }_{18} \mathrm{Ar}^{40} .\) This is because \({ }_{19} \mathrm{~K}^{40}\) has tendency to undergo (a) \(\alpha\) decay (b) positronium decay (c) \(\beta\) decay (d) \(\gamma\) decay

Step-by-Step Solution

Answer

\(\beta^+\) decay (positron emission or electron capture) transforms \({ }_{19} \mathrm{~K}^{40}\) into \({ }_{18} \mathrm{Ar}^{40}\).

Step 1: Understand the Isotopes

The isotopes mentioned are \({ }_{19} \mathrm{~K}^{40}\) and \({ }_{18} \mathrm{Ar}^{40}\). Isotopes are atoms with the same number of protons but different numbers of neutrons. Potassium-40 (K-40) and Argon-40 (Ar-40) have different proton counts.

Step 2: Analyze The Given Process

Potassium-40 is transforming into Argon-40. This involves a decrease in proton count from 19 in potassium to 18 in argon, while the atomic mass remains constant at 40.

Step 3: Recognize Suitable Decay Processes

Identify possible decay processes that could result in this transformation:1. **\(\alpha\) Decay** would reduce the mass number by 4.2. **Positron Emission (a type of \(\beta\) decay)** and Electron Capture can decrease the proton number by 1.3. **\(\beta^-\) Decay** would increase the proton number by 1.4. **\(\gamma\) Decay** affects energy states but not nucleus particle count.

Step 4: Select the Appropriate Process

In the transformation of \({ }_{19} \mathrm{~K}^{40}\) to \({ }_{18} \mathrm{Ar}^{40}\), the proton number decreases by 1 with no mass number change, which is characteristic of positron emission or electron capture, both part of \(\beta^+\) decay. Thus, the correct answer is (b) positronium decay.

Key Concepts

Isotopes

Isotopes are fascinating variants of chemical elements. While isotopes of the same element share the same number of protons, they have different numbers of neutrons. This variance in neutron number gives isotopes unique atomic mass while retaining identical chemical properties. For example, in the case of

• Potassium-40 ( _{19} K^{40}), there are 19 protons and 21 neutrons.
• Argon-40 ( _{18} Ar^{40}), in contrast, possesses 18 protons and 22 neutrons.

Despite the difference in neutron count, both isotopes share a mass number of 40. This shared characteristic plays a pivotal role in nuclear reactions, influencing how elements undergo decay processes. Understanding isotopes is crucial since they determine how matter interacts both chemically and physically in nuclear reactions.

Beta Decay

Beta decay is a fundamental concept in nuclear chemistry, playing a key role in explaining the transformation of isotopes. This type of decay involves the conversion of a neutron into a proton, or vice versa, within an atomic nucleus with the emission of particles. Within beta decay, we have two main processes:

• **Beta-minus (\(β^-\)) decay:** A neutron turns into a proton while emitting an electron and an antineutrino. This results in an increase in the atomic number by 1.
• **Beta-plus (\(β^+\)) decay or positron emission:** A proton is converted into a neutron, releasing a positron and a neutrino, thus decreasing the atomic number by 1.

An example of beta decay is the decay of Potassium-40 into Argon-40, which can occur through positron emission. Understanding beta decay is crucial, as it explains how elements change into different elements naturally, influencing radioactive processes significantly.

Positron Emission

Positron emission is a specific subtype of beta decay, also known as beta-plus (\(β^+\)) decay. During this process, a proton within the nucleus is converted into a neutron. This conversion accompanies the emission of a positron (the antimatter counterpart of the electron) and a neutrino. A characteristic feature of positron emission includes:

• A decrease in the atomic number by 1.
• The mass number remains unchanged.
• The emitted positron soon encounters an electron, resulting in annihilation and the release of gamma rays.

Positron emission is essential in nuclear chemistry, especially in understanding how elements like Potassium-40 transform into Argon-40. This type of decay effectively tracks how an element transitions into another by lowering its proton count, without altering its overall atomic weight.

Nuclear Chemistry

Nuclear chemistry is the study of reactions and changes that occur in atomic nuclei. It covers many fascinating phenomena including radioactive decay, nuclear reactions, and the properties of isotopes. Key processes in nuclear chemistry include:

• **Radioactive Decay:** Spontaneous transformation of an unstable nucleus into a stable one, releasing energy.
• **Fission and Fusion:** Processes that involve splitting or combining atomic nuclei, releasing vast amounts of energy.
• **Isotope Applications:** Usage of isotopes in fields like medicine (e.g., PET scans using positron-emitting isotopes) and archaeology (e.g., carbon dating).

Understanding nuclear chemistry allows us to harness energy from nuclear reactions, develop medical technologies, and comprehend natural processes that occur within stars. By studying nuclear transformations, such as in the Potassium-40 decay, we gain insights not only into the makeup and behavior of atoms but also into the evolution of matter in our universe.