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

Emission of a positron (c).

Step 1: Analyze the problem

Examine the transformation from \(_7N^{13}\) to \(_6C^{13}\). Notice that nitrogen loses one proton, changing into carbon, with the mass number remaining 13.

Step 2: Understand identity changes

Identify that a decrease in atomic number (from 7 to 6) implies the emission of a particle that changes proton into neutron.

Step 3: Identify the type of radiation

Recall that the emission of a positron results in the conversion of a proton into a neutron, thereby reducing the atomic number by one.

Step 4: Conclusion

The change from \(_7N^{13}\) to \(_6C^{13}\) is due to the emission of a positron, as it decreases the proton count and increases the neutron count accordingly.

Key Concepts

Radioactive Decay

Radioactive decay is a spontaneous process where an unstable atomic nucleus loses energy by emitting radiation. During this process, the nucleus of an atom changes to form a different isotope or element. This transformation can involve the release of various types of particles such as alpha particles, beta particles, or gamma rays. Radioactive decay follows a random process, but it can be characterized by a half-life, which is the time it takes for half of the radioactive nuclei in a sample to decay. This natural phenomenon plays a crucial role in nuclear chemistry, influencing everything from dating archaeological finds to powering nuclear reactors. In the case of the problem, radioactive decay is demonstrated by the transformation of nitrogen ( _7N^{13} ) to carbon ( _6C^{13} ). This change involves the emission of a positron, a specific type of beta particle, making the process identifiable as beta-plus decay which is a subcategory of radioactive decay.

Positron Emission

Positron emission is a type of beta decay where a proton in the nucleus is transformed into a neutron, releasing a positron in the process. A positron is the antimatter counterpart of an electron with the same mass but opposite charge. When a nucleus emits a positron:

• The atomic number decreases by one, as a proton is converted into a neutron.
• The neutron count increases, while the overall mass number remains unchanged.
• The result is the transformation into a different element.

Understanding positron emission is essential for interpreting certain nuclear reactions and applications such as in Positron Emission Tomography (PET) scans, a medical imaging technique. In the exercise, _7N^{13} emits a positron, leading to its transformation into _6C^{13} . This highlights the nature of positron emission in altering the identify of the nucleus.

Nuclear Reactions

Nuclear reactions involve a change in an atom's nucleus and can result in the transformation of one element into another. These reactions require significant amounts of energy compared to chemical reactions that involve electron exchanges. In nuclear chemistry:

• Atoms collide at high speeds, causing changes in the nuclear structure.
• Elements can convert into different isotopes or completely new elements.
• Nuclear reactions can be either spontaneous or induced.

Typically, nuclear reactions include fission, fusion, or radioactive decay processes like that in the provided exercise. The problem illustrates a nuclear reaction where the nitrogen nucleus undergoes radioactive decay by emitting a positron, resulting in the formation of a carbon atom.

Atomic Number Change

The atomic number signifies the number of protons in an atom's nucleus and determines the element's identity. Changes in atomic number occur as a result of nuclear processes, impacting which element an atom represents. In particular:

• A decrease in atomic number indicates a reduction in the proton count.
• The transformation involves converting a proton into a neutron, often through positron emission.
• The mass number, which is the total of protons and neutrons, usually remains the same during such changes.

These reactions reveal fundamental aspects of nuclear transformations and element stability. The exercise demonstrates this by showing _7N^{13} changing to _6C^{13} , highlighting how emitting a positron results in the atomic number decreasing by one, altering nitrogen to carbon while keeping the mass number constant.