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: n/p ration decreases (d) \(\alpha\) - decay: \(\mathrm{n} / \mathrm{p}\) ratio increases

Short answer

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

Step-by-step solution

Understanding Positron Emission

In positron emission, a proton in the nucleus is converted into a neutron while emitting a positron. This action leads to a decrease in the number of protons and an increase in the number of neutrons, hence the neutron-to-proton (n/p) ratio increases. Therefore, statement (a) is correctly matched.

Analyzing K-Electron Capture

K-electron capture occurs when an electron from the innermost energy level (K-shell) is captured by the nucleus, converting a proton into a neutron. This increases the number of neutrons and decreases the number of protons, resulting in an increased n/p ratio. Therefore, statement (b) is incorrectly matched as it decreases n/p.

Interpreting Beta Decay

Beta decay involves the transformation of a neutron into a proton with the emission of a beta particle (an electron), thus decreasing the neutron count and increasing the proton count. This results in the decrease of the n/p ratio. Hence, 2 c) is correctly matched.

Examining Alpha Decay

During alpha decay, the nucleus emits an alpha particle (2 neutrons and 2 protons), leading to a simultaneous decrease in both neutrons and protons. Given their common reduction, the n/p ratio remains relatively stable and does not necessarily increase. Therefore, statement (d) is incorrectly matched.

Key concepts

Positron Emission

Positron emission is a fascinating process in nuclear reactions. In this process, a proton inside the nucleus is transformed into a neutron. During this transformation, a positron is emitted. A positron is the antimatter counterpart of an electron, having the same mass but opposite charge. This proton-to-neutron conversion reduces the atomic number by one while leaving the atomic mass nearly unchanged.

This process causes an increase in the neutron-to-proton (n/p) ratio because the number of protons decreases while the number of neutrons increases. Positron emission is common in lighter elements where the nucleus has too many protons. It helps the atom achieve a more stable state.

Examples of elements that can undergo positron emission include certain isotopes of carbon and nitrogen. Understanding this process is crucial in fields like medical imaging, particularly in positron emission tomography (PET scans), which utilize this phenomenon for diagnostics.

K-Electron Capture

K-electron capture is another intriguing nuclear reaction. This process involves an electron from the K-shell, which is the innermost electron shell, being captured by the nucleus. In this event, the captured electron combines with a proton to form a neutron. The atomic number decreases as the proton count is reduced, turning into a neutron, while the mass number remains constant.

Despite the expectation that losing a proton would decrease the n/p ratio, the conversion of a proton into a neutron actually increases this ratio. The reduction of protons and simultaneous increase of neutrons makes the n/p ratio larger, contributing to a more stable nucleus, especially in cases where the element has too many protons for stability.

K-electron capture is observed in heavier elements and can affect how isotopes decay over time. This process is significant in understanding the chemical behavior of elements and the stability of isotopes, playing a role in both astrophysical processes and radioactive decay sequences.

Beta Decay

Beta decay is a process where a neutron turns into a proton while emitting a beta particle, which is an electron in this case. This transformation results in an increase in the number of protons and a decrease in the number of neutrons.

This change effectively reduces the neutron-to-proton (n/p) ratio, as there are now more protons relative to neutrons in the nucleus. Beta decay is common in scenarios where there is an excess of neutrons, helping balance the n/p ratio closer to stability.

The process is significant in the decay series of many radioactive elements and is crucial in nuclear physics and atomic energy production. Beta particles emitted during this decay carry negative charge and high energy. They can pass through materials, making them detectable and usable in various applications like radiation therapy and nuclear medicine.

Alpha Decay

Alpha decay is characterized by the emission of an alpha particle from the nucleus. An alpha particle consists of 2 protons and 2 neutrons, equivalent to a helium nucleus. This simultaneous reduction in both protons and neutrons does not significantly alter the neutron-to-proton (n/p) ratio; instead, it reduces the overall size of the nucleus.

The loss of an alpha particle decreases the atomic number by two and the mass number by four, shifting the element two places back on the periodic table. Alpha decay is typical in very heavy elements, helping them move toward greater nuclear stability by removing surplus nucleons.

Understanding alpha decay is important in radiometric dating, nuclear waste management, and the study of nuclear chain reactions. Due to the double positive charge of alpha particles, they interact strongly with materials and have low penetration power, making them easy to block with simple barriers.