Problem 118 - A Complete Resource Book in Chemistry for JEE Main

Question

Which is/are correctly matched? (a) Positron emission : \(\mathrm{n} / \mathrm{p}\) ration increases (b) \(\mathrm{K}\) - electron capture : \(\mathrm{n} / \mathrm{p}\) decreases (c) \(\beta\) - decay : \(\mathrm{n} / \mathrm{p}\) ration decreases (d) \(\alpha-\) decay : \(\mathrm{n} / \mathrm{p}\) ratio increases

Step-by-Step Solution

Answer

Options (a) and (c) are correctly matched.

Step 1: Understanding Positron Emission

In positron emission, a proton in the nucleus is converted into a neutron and a positron, which is ejected from the nucleus. This process decreases the atomic number by one and increases the neutron-to-proton ratio ( / p"). Therefore, option (a) is correctly matched as the n/p ratio increases.

Step 2: Analyzing K-electron Capture

K-electron capture occurs when an inner-electron (typically from the K-shell) is captured by the nucleus, converting a proton into a neutron. This process increases the n/p ratio because the number of neutrons increases while the number of protons decreases. Therefore, option (b) is incorrectly matched since n/p increases, not decreases.

Step 3: Evaluating Beta Decay

During β-decay, a neutron is converted to a proton with the emission of a beta particle. This increases the atomic number by one and decreases the neutron-to-proton ratio. Thus, / p" ratio decreases during β-decay, making option (c) correctly matched.

Step 4: Assessing Alpha Decay

In alpha decay, a nucleus emits an alpha particle (two neutrons and two protons), reducing both the number of neutrons and protons in the nucleus. The n/p ratio depends on the original distribution in the nucleus, but generally, alpha decay doesn't necessarily increase n/p ratio. Based on typical decay series, option (d) does not consistently increase n/p ratio, making it an incorrect match.

Key Concepts

Positron Emission

In the process of positron emission, a proton in the nucleus transforms into a neutron and then releases a positron. A positron is essentially the positively charged counterpart of an electron. This emission causes the atomic number of the element to decrease by one while the mass number remains unchanged.
Consequently, the neutron-to-proton ratio in the nucleus increases, which balances the nucleus when there are too many protons.
Understanding this process is crucial because it illustrates how the number of protons and neutrons can change without altering the mass number.
Positron emission often occurs in proton-rich, or neutron-deficient, radioactive nuclei.
When compared with other types of decay processes, positron emission highlights nature's balance in stabilizing the atomic nucleus by adjusting its internal composition.

K-electron Capture

K-electron capture, also known as electron capture, is a process where an electron from the closest energy level (the K-shell) is captured by the nucleus. In this reaction, a proton combines with the captured electron to form a neutron. This results in a transformation where the atomic number decreases by one, and like positron emission, the mass number stays the same.
This process is essential when discussing nuclear stability as it increases the neutron-to-proton ratio. It helps stabilize atoms with too many protons by converting some of them into neutrons.
K-electron capture is a natural occurrence in many radioactive isotopes, especially those with a proclivity for gaining stability through a different form of decay rather than positron emission.
It is a critical process for understanding how elements change identity and achieve stability without altering the overall mass of the nucleus.

Beta Decay

Beta decay is a fascinating radioactive process where a neutron in the nucleus is transformed into a proton, releasing a beta particle and an antineutrino. This decay causes the atomic number to increase by one and decreases the neutron-to-proton ratio.
The transformation discovered here is amazingly efficient for elements with too many neutrons, shifting the balance towards more stable forms.
This leads to the conversion of a neutron ( ) into a proton ( ), emitting a high-speed electron known as a beta particle. Hence, the identity of the nucleus changes.
Interestingly, beta decay highlights how radioactive atoms can alter in response to internal imbalance by shedding excess neutrons while simultaneously increasing their atomic number. The concept of beta decay is crucial for understanding the formation of new elements in nature.

Alpha Decay

Alpha decay involves the emission of an alpha particle from the nucleus. An alpha particle is comprised of two protons and two neutrons, effectively like a helium nucleus. When an atom undergoes alpha decay, its atomic number decreases by two and its mass number decreases by four.
This process affects both protons and neutrons equally, leading usually to a larger decrease in atomic size and change in atomic number. During the process of alpha decay, the ratio of neutrons to protons is altered, but the change depends on the original configuration.
In many cases, the balance doesn't consistently favor an increase in the ratio, making alpha decay unique in its role of changing both elemental identity and mass significantly.
Alpha decay provides insight into the ways nuclei achieve stability when they are simply too large or have too many nucleons clumped together. It's a fundamental concept in the study of radioactive decay and nuclear chemistry.