Problem 2 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

A positron is emitted from \({ }_{11}^{23} \mathrm{Na}\). The ratio of the atomic mass and atomic number of the resulting nuclide is (a) \(22 / 10\) (b) \(22 / 11\) (c) \(23 / 10\) (d) \(23 / 12\)

Step-by-Step Solution

Answer

(c) 23/10

Step 1: Understanding Positron Emission

In positron emission, a proton in the nucleus is converted into a neutron and a positron is emitted. This decreases the atomic number by one but does not change the mass number since a neutron and a proton have nearly the same mass.

Step 2: Identify Changes in Atomic and Mass Numbers

The initial nuclide is \( _{11}^{23} \text{Na} \). Upon positron emission:- The atomic number decreases by one: \(11 - 1 = 10\).- The mass number remains the same: \(23\).

Step 3: Calculate the Ratio

The resulting nuclide has an atomic mass \(A = 23\) and an atomic number \(Z = 10\). Therefore, the ratio of the atomic mass to the atomic number is \( \frac{23}{10} \).

Step 4: Select the Correct Option

Comparing the calculated ratio \( \frac{23}{10} \) with the provided options, we see that option (c) \( \frac{23}{10} \) is the correct choice.

Key Concepts

Positron Emission

Positron emission is a type of nuclear reaction where a proton in an atomic nucleus is transformed into a neutron, and a positron is emitted. This is one of the processes of beta decay and is referred to as beta plus decay. When the positron is emitted, it can be thought of as an "anti-electron" because it has the same mass as an electron but a positive charge.
This process is common in proton-rich nuclides, where there are too many protons relative to neutrons. When a positron is emitted, the atomic nucleus becomes more stable because the proton-to-neutron ratio is more balanced.

• It decreases the atomic number by one.
• The mass number remains unchanged since the neutron and proton have almost identical masses.

For example, when sodium-23 ( _{11}^{23} ext{Na}) undergoes positron emission, it converts into a different element altogether.

Atomic Number

The atomic number of an element, denoted by the symbol Z, is fundamental in determining the identity of an element. It represents the number of protons in the nucleus of an atom. Each element in the periodic table has a unique atomic number, which defines its properties and its position in the periodic table.
In the process of positron emission, the atomic number is crucial because it tells us how the identity of the element changes. During positron emission:

• The atomic number decreases by one because a proton becomes a neutron.
• The identity of the element changes since each element has a distinct atomic number.

In the given example with sodium-23, the initial atomic number is 11, and after positron emission, it changes to 10, indicating a transformation into a different element.

Mass Number

The mass number is a total count of the number of protons and neutrons in an atomic nucleus and is represented by the symbol A. Unlike the atomic number, the mass number does not define the identity of an element but rather its isotopes.
In nuclear reactions, the mass number is vital for identifying how a nucleus changes, especially how its composition of protons and neutrons adjusts during processes like nuclear decay.

• During positron emission, the mass number remains constant.
• The transformation occurs internally as a proton changes into a neutron.

For sodium-23, the mass number remains at 23 both before and after the positron emission. This stability in the mass number is why we only see a change in atomic identity but not in isotope identity.

Nuclear Decay Process

Nuclear decay processes are transformations that lead to changes in the energy level, structure, or identity of an atomic nucleus. These processes often result in the emission of particles or radiation. Positron emission is one such nuclear decay process, specifically used by proton-rich nuclei to achieve stability.
The characteristics of nuclear decay include:

• Changes that adjust the proton-to-neutron ratio to reach a stable configuration.
• Emission of particles like positrons, which help reduce proton excess.
• Transformation of the element due to changes in atomic number.

In the given example, sodium-23 undergoes nuclear decay via positron emission, resulting in the production of a different element with an adjusted atomic number and a more stable nuclear composition.