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

(a) and (c) are correctly matched.

Step 1: Understanding the decay processes

Before evaluating the options, let's understand the different nuclear decay processes. In positron emission, a proton is transformed into a neutron, thereby decreasing the proton number which generally increases the neutron-to-proton (n/p) ratio. In K-electron capture, an inner electron is captured by the nucleus causing a proton to become a neutron, also increasing the n/p ratio by reducing the number of protons. In β-decay (beta-minus decay), a neutron is converted into a proton, thus increasing the proton number and decreasing the n/p ratio. In α-decay, an alpha particle (2 protons and 2 neutrons) is emitted. While both protons and neutrons decrease, they do not always change the n/p ratio significantly compared to positron emission or beta decay.

Step 2: Analyzing option (a)

In positron emission, the proton count decreases while neutrons increase, which causes an increase in the n/p ratio. Therefore, option (a) is correctly matched.

Step 3: Analyzing option (b)

For K-electron capture, a proton is converted to a neutron, thus increasing the number of neutrons and decreasing the number of protons, which results in an increased n/p ratio. Therefore, option (b) is incorrectly matched because it said n/p ratio decreases.

Step 4: Analyzing option (c)

In β-decay, a neutron is converted into a proton, thus increasing the number of protons and decreasing the number of neutrons, leading to a decrease in the n/p ratio. Therefore, option (c) is correctly matched.

Step 5: Analyzing option (d)

In α-decay, the removal of 2 protons and 2 neutrons should technically reduce both the neutron and proton numbers equivalently, often not increasing the n/p ratio significantly unless in specific isotopes. Therefore, option (d) is incorrectly matched if generalized.

Key Concepts

Positron Emission

Positron emission is a process where a proton in the nucleus transforms into a neutron and emits a positron, which is the antimatter counterpart of an electron. This process is a type of beta-plus decay and occurs in proton-rich nuclei.

• The proton changes to a neutron, thereby decreasing the number of protons in the nucleus.
• The emission of the positron balances the charge imbalance from the proton’s conversion.
• By decreasing the proton count while the neutron count remains the same, the neutron-to-proton ( /p) ratio increases.

This change helps stabilize the nucleus if it has too many protons, making positron emission vital for balancing the atomic structure in certain isotopes.

Beta Decay

Beta decay is another type of decay process where a neutron is converted into a proton, and in doing so, a beta particle is emitted. Often known as beta-minus decay, this process reduces the neutron-to-proton ( /p) ratio.

• A neutron, which is neutral, changes into a positive proton.
• It releases a beta particle or electron in the process to maintain balance in charge.
• The increase in protons and the concurrent decrease in neutrons results in a lower /p ratio.

Beta decay is commonly seen in neutron-rich isotopes where the conversion helps stabilize the nucleus by turning an excess neutron into a proton.

Alpha Decay

Alpha decay occurs when an unstable nucleus releases an alpha particle, which is composed of 2 protons and 2 neutrons. This type of decay is typical with very heavy elements.

• The emission of the alpha particle reduces both the atomic mass and atomic number of the original element.
• The reduction affects the number of both protons and neutrons equally, often not significantly altering the /p ratio.

This process helps reduce nuclear mass, aiding in stability, although its effect on the /p ratio is generally minimal unless in specific isotope cases.

K-Electron Capture

K-electron capture is a unique process where an electron from the innermost shell is captured by the nucleus. This electron combines with a proton to form a neutron.

• The captured electron effectively turns a proton into a neutron, reducing the total proton count.
• As the number of protons decrease and neutrons increase, the /p ratio tends to increase.

This process usually occurs in proton-heavy nuclei where a reduction in proton count helps stabilize the atomic nucleus by increasing the /p ratio.