Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

An artificial radioactive isotope has \({ }_{7} \mathrm{~N}^{14}\) after two successive \(\beta\) particle emissions. The number of neutrons in the parent nucleus must be (a) 14 (b) 9 (c) 7 (d) 5

Step-by-Step Solution

Answer

The number of neutrons in the parent nucleus must be 9.

Step 1: Understanding Beta Decay

In beta (\( \beta^- \)) decay, a neutron in the nucleus transforms into a proton and an electron (beta particle) is emitted. This process increases the atomic number (number of protons, \( Z \)) by one, but the mass number (sum of protons and neutrons, \( A \)) remains the same.

Step 2: Analyzing Successive Emissions

Since \({_7}^N^{14}\) is the resultant nucleus after two successive \( \beta^- \) emissions, each emission increases the proton number by one. The original parent nucleus must therefore have had two fewer protons. Thus, the original proton number was \(7 - 2 = 5\).

Step 3: Finding Neutron Count in Parent Nucleus

Knowing the parent nucleus had a proton number of 5 and that its mass number \( A = 14 \) (because this doesn't change), the neutron number \( N \) is given by \( N = A - Z = 14 - 5 = 9 \).

Step 4: Conclusion

The parent nucleus had 9 neutrons, as calculated by subtracting the proton number from the mass number.

Key Concepts

Beta Decay

Beta decay is a fundamental process in nuclear chemistry. It occurs when a nucleus is unstable and seeks to achieve stability through the transformation of a neutron into a proton and the emission of a beta particle (electron). This is known specifically as beta-minus (\( \beta^- \)) decay.

• During this process, the atomic number (\( Z \)) of the element increases by 1, because a new proton is added to the nucleus.
• However, the mass number (\( A \)) remains unchanged, since the total count of nucleons (protons + neutrons) does not vary.

This concept is crucial to understanding how certain elements transform into others during radioactive decay.

Neutron Count

The neutron count or the number of neutrons in a nucleus is vital for determining the stability and identity of an isotope. Neutrons, alongside protons, make up the atomic nucleus, and their count influences the overall mass number.

• To calculate the number of neutrons (\( N \)) in a nucleus, subtract the number of protons (\( Z \)) from the mass number (\( A \)).
• Mathematically, this can be expressed as \( N = A - Z \).

In nuclear chemistry, determining the neutron count can help predict the behavior of a nucleus during reactions like beta decay.

Parent Nucleus

A parent nucleus refers to the original nucleus before it undergoes transformation in radioactive decay processes, such as beta decay. Understanding the parent nucleus is essential for tracking changes that occur during nuclear reactions.

• The parent nucleus contains the original number of protons and neutrons before any decay events.
• Its characteristics, such as proton and neutron count, help predict the resulting daughter nucleus after decay.

After beta decay, the parent nucleus will have transformed, but the mass number remains constant, aiding in the identification of the parent by working backwards from the daughter nucleus's atomic structure.

Artificial Radioactive Isotope

Artificial radioactive isotopes are isotopes that have been artificially created or altered by humans, often in nuclear reactors or particle accelerators. These isotopes are not typically found in significant quantities in nature.

• They are often used in medicine for diagnostics and treatment, as well as in scientific research.
• Many of these isotopes are created by inducing reactions such as beta decay to study their properties or practical applications.

Understanding both the creation and decay processes of artificial isotopes, like the one transitioning to a \( {}_7 \mathrm{~N}^{14} \), provides insight into broader nuclear processes and aids in advancements across various scientific fields.