Problem 124 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements is/are incorrect, when the nuclide, \({ }_{19} \mathrm{~K}^{40}\), is subject to \(\mathrm{K}\)-electron capture? (a) \({ }^{40} \mathrm{Ar}\) is produced with emission of \(\beta\)-particle. (b) \({ }^{40} \mathrm{Ar}\) is produced with emission of \(\alpha\)-particles. (c) \({ }^{40} \mathrm{Ar}\) is produced without emission of radiation (d) \({ }^{40} \mathrm{Ar}\) is produced with emission of X-radiation.

Step-by-Step Solution

Answer

Statements (a), (b), and (c) are incorrect.

Step 1: Understanding K-electron Capture

K-electron capture, also known as K-capture, is a process where an electron from the innermost energy level (K-shell) is captured by the nucleus of an atom. In this process, a proton in the nucleus is converted into a neutron, resulting in a decrease in the atomic number by 1 but keeping the mass number the same.

Step 2: Analyzing the Nuclide Transformation

For the nuclide ({}_{19} ext{K}^{40} ), K-electron capture will convert a proton into a neutron, transforming it into ({}_{18} ext{Ar}^{40} ). This is because the atomic number decreases by 1 (from 19 to 18), but the mass number (40) remains unchanged.

Step 3: Checking for Emission of Particles or Radiation

(a) states emission of a β-particle. This isn't correct in K-electron capture which involves emission of neutrinos and x-rays rather than β-particles. (b) suggests emission of α-particles, which occurs in alpha decay, not K-electron capture. (c) states no radiation emission, but K-electron capture often emits x-radiation. (d) proposes emission of X-radiation, which can occur due to reorganization of electrons post-capture.

Step 4: Identifying Correct and Incorrect Statements

Based on the understood process, statements (a) and (b) are incorrect: (a) due to incorrect emission type and (b) because α-particles are not emitted during K-electron capture. Statement (c) is incorrect because x-radiation can occur. Statement (d) is correct as X-rays may be produced.

Key Concepts

Nuclide Transformation

When we talk about nuclide transformation, it's important to understand that it refers to the change that occurs in a nucleus when a nuclear process happens, such as K-electron capture. In this specific case, you start with potassium-40, represented as - \(_{19} \mathrm{K}^{40}\) During K-electron capture, this nuclide undergoes a transformation. It captures an electron from its own K-shell (the closest shell to the nucleus). This captured electron combines with a proton, and as a result of this reaction, the proton is transformed into a neutron. This process decreases the atomic number by 1, as you are losing one proton, but the mass number stays the same because a neutron is gained. Therefore, the potassium nuclide is transformed into an argon nuclide: - \(_{18} \mathrm{Ar}^{40}\)This is the essence of nuclide transformation during a K-electron capture process.

K-shell Electron

The K-shell refers to the innermost electron orbit closest to the nucleus in an atom. This shell is the first level from the nucleus, and it holds the electrons most strongly attracted to the nucleus. The K-electron capture process specifically involves an electron from this shell. During the capture: - An electron from the K-shell is drawn into the nucleus. - This electron reacts with a proton. - It turns the proton into a neutron. This is critical because altering the proton count in a nucleus changes the identity of the atom. Without the capture of the K-shell electron, the subsequent nuclide transformation would not occur. The inner K-shell electron plays a pivotal role in allowing the atom to undergo this type of transformation.

Emission of Radiation

After K-electron capture, the atom often undergoes electronic rearrangement. This happens because of the vacancy left by the captured K-shell electron. To fill this gap, electrons from higher energy levels jump down, and this energy reorganization leads to the emission of X-rays. Here’s how it unfolds: - The captured electron leaves a vacancy in the K-shell. - Other electrons fall into this vacancy from higher energy levels (like L or M shells). - The transition of these electrons releases energy in the form of X-rays. This emission is characteristic of K-electron capture and identifies that radiation is indeed released, contrary to certain misconceptions about the process being radiation-free.

Atomic Number and Mass Number Change

It's important to consider how the atomic number and mass number are affected during K-electron capture. - **Atomic Number Change**: In K-electron capture, the atomic number decreases by 1. This happens because a proton in the nucleus is converted into a neutron. For example, potassium changes from \ - \(_{19} \mathrm{K}\) \ to \ - \(_{18} \mathrm{Ar}\). - **Mass Number Change**: Notably, the mass number remains the same. This is because, while a proton is lost, a neutron is gained, effectively keeping the total count of nucleons (protons + neutrons) the same. These changes ensure the identity of the element changes (since elements are defined by their atomic numbers), while the overall atomic mass remains unaltered. Understanding this balance between atomic transformation and mass conservation is key to grasping how K-electron capture affects an atom’s nucleus.