Problem 47 - A Complete Resource Book in Chemistry for JEE Main

Question

\({ }_{7} \mathrm{~N}^{13}\) changes to \({ }_{6} \mathrm{C}^{13}\) by emission of (a) electron (b) neutron (c) positron (d) proton

Step-by-Step Solution

Answer

The emission is (c) positron.

Step 1: Understand the Initial and Final Nuclei

We start with an atom \({ }_{7} \mathrm{~N}^{13}\), which means it has 7 protons and a mass number of 13. It changes to \({ }_{6} \mathrm{C}^{13}\), indicating it now has 6 protons but the same mass number of 13.

Step 2: Compare Proton Numbers

The initial nucleus has 7 protons, while the final nucleus has 6 protons. This indicates a change where the number of protons reduces by 1.

Step 3: Determine the Type of Emission

A decrease in the number of protons (from 7 to 6) while maintaining the same mass number (13) suggests an emission that transforms a proton into a neutron. This is characteristic of positron emission, where a proton turns into a neutron, emitting a positron.

Key Concepts

Positron Emission

Positron emission is a type of nuclear decay where an unstable nucleus transforms by converting one of its protons into a neutron.
This process is accompanied by the emission of a positron, which is the antimatter counterpart of the electron and carries a positive charge.
Positron emission is a common way for isotopes with too many protons to stabilize. The nuclear equation for positron emission can be represented as:

• A proton in the nucleus is converted into a neutron.
• A positron (β⁺) and a neutrino are emitted.

Using the exercise as an example,

• The nitrogen-13 ( { }_{7} ext{N}^{13}) nucleus emits a positron and becomes carbon-13 ( { }_{6} ext{C}^{13}).
• The number of protons decreases by one, transforming nitrogen into carbon.

Positron emission helps the nucleus reach a more stable state by adjusting the balance between protons and neutrons.

Proton to Neutron Transformation

The transformation of a proton into a neutron is a crucial part of certain types of radioactive decay, such as positron emission.
This process ensures that the nucleus becomes more energetically stable, especially when there is an excess of protons. In the proton to neutron transformation:

• One proton is lost from the nucleus, while one neutron is gained, maintaining a balance.
• This change does not affect the atomic mass but changes the atomic number.

Referring to the nitrogen to carbon transition:

• The proton number drops from 7 in nitrogen (resulting in carbon with 6 protons).
• There is no change in the mass number, which remains at 13, indicating stability in relative isotopic mass.

Through this process, elements can transmogrify from one type to another while generally adhering to the conservation laws.

Mass Number Conservation

The principle of mass number conservation states that the total mass number before and after a nuclear reaction must remain the same.
This is a key concept in nuclear reactions, ensuring that the sum of protons and neutrons (mass number) in the reactants equals that in the products. During nuclear decay, such as positron emission:

• The mass number doesn't change even as an element transforms.
• A proton is converted to a neutron, hence the overall mass number (sum of protons and neutrons) is conserved.

In our example:

• Nitrogen-13 ( { }_{7} ext{N}^{13}) changes to carbon-13 ( { }_{6} ext{C}^{13}), yet the mass number remains constant at 13.
• This showcases how nuclear transformations honor the mass number, despite changes in the atomic structure.

Thus, mass number conservation allows for a stable outcome in nuclear processes, providing consistency across nuclear transformations.