Problem 60 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

The emission is of a positron.

Step 1: Understanding the Problem

We have an isotope of nitrogen, \(_{7} \mathrm{~N}^{13}\), that changes into an isotope of carbon, \(_{6} \mathrm{C}^{13}\), by emitting a particle. We need to determine which particle (proton, electron, neutron, or positron) is emitted during this process.

Step 2: Analyze Initial and Final Elements

The initial element is nitrogen with 7 protons, and the final element is carbon with 6 protons. The mass number remains the same at 13, but the atomic number decreases by 1.

Step 3: Determine the Emitted Particle

Since the atomic number decreases by 1 (from 7 to 6) while the mass number remains the same, a positive charge of +1 must have been removed to maintain the overall charge balance. This indicates the emission of a positron because the emission of a positron involves the conversion of a proton into a neutron, conserving the mass number and decreasing the atomic number by 1.

Step 4: Conclusion

The transformation from \(_{7} \mathrm{~N}^{13}\) to \(_{6} \mathrm{C}^{13}\) involves the emission of a positron, resulting in the loss of a proton without changing the mass number.

Key Concepts

Radioactive Decay

Radioactive decay is a fascinating process through which unstable atomic nuclei lose energy by emitting radiation. This emission occurs naturally and is crucial to understanding the stability of different elements. There are several types of radioactive decay, including alpha, beta, and gamma decay. In each case, the nucleus releases particles or energy to become more stable.

In the context of our example, radioactive decay is evident as nitrogen changes into carbon. The important thing to note is that radioactive decay can alter the identity of an atom by changing its atomic number, while sometimes maintaining its mass number. This transformation underscores the natural quest of nuclei to reach a more stable state. Understanding radioactive decay is pivotal in nuclear chemistry, as it helps us predict and explain the behavior of isotopes over time.

Positron Emission

Positron emission is a type of radioactive decay in which a proton inside the nucleus of an atom is converted into a neutron while releasing a positron and a neutrino. A positron is essentially the antimatter counterpart of an electron, possessing the same mass but with a positive electric charge.

When nitrogen-13 decays into carbon-13, it undergoes positron emission. This process decreases the atomic number by one, transforming the atom into a different element. It conserves the mass number, as the total number of nucleons (protons and neutrons) remains unchanged. This type of decay not only alters the atomic composition but also emits a positron, which promptly interacts with electrons, leading to annihilation and the release of energy. Positron emission is a fascinating example of the subatomic transformations that elements can undergo during nuclear decay.

Isotopes

Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nuclear mass. However, they share the same number of protons in the nucleus, giving them identical chemical properties. The distinction of isotopes lies in their mass number, which is the sum of protons and neutrons.

For example, nitrogen-13 and carbon-13 are isotopes differing in their proton count. The study of isotopes extends beyond just recognizing differences; it involves understanding their stability and the modes of decay they may undergo. Some isotopes are stable, while others are prone to decay, affecting their presence and longevity.

• Stable isotopes do not change over time.
• Unstable isotopes may undergo radioactive decay to achieve stability.

The science of isotopes is crucial in many fields such as medicine, where radioactive isotopes are used in diagnostic imaging, and in environmental science, where isotopic compositions help trace processes and sources. Understanding isotopes is central to mastering nuclear chemistry and grasping the intricate processes of atomic change.