Problem 82 - 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 is 9 (option b).

Step 1: Understand Beta Decay

During beta decay, a neutron in the nucleus is transformed into a proton, emitting a beta particle (an electron) and an antineutrino. This process increases the atomic number by one but keeps the mass number unchanged.

Step 2: Analyze Given Information

We know that \[_{7}^{14}\text{N} \] is the result of two beta decays. The final nucleus configuration after the decays is nitrogen with an atomic number of 7 and a mass number of 14.

Step 3: Reverse Engineer the Beta Decays

If we reverse the beta decay process, the atomic number before the decays was 5. This is because each beta decay increased the atomic number by one: 5 + 2 = 7.

Step 4: Calculate Number of Neutrons in Parent Nucleus

The mass number was 14, and the atomic number was 5 before any decay started. The number of neutrons in the nucleus can be found by subtracting the atomic number from the mass number: \( n = A - Z = 14 - 5 = 9 \).

Key Concepts

Artificial Radioactive Isotope

An artificial radioactive isotope is a human-created version of a naturally occurring element that is unstable and emits radiation. These isotopes are typically created in laboratories or nuclear reactors through processes like neutron activation. In the given exercise, the concept revolves around beta decay, which is a type of radioactive decay where an isotope emits beta particles.
This process involves the conversion of a neutron into a proton, transforming the element into a different one. For instance, the isotope in the exercise is initially created through a process that doesn't occur naturally. It begins with a parent nucleus that changes due to radioactive decay. Understanding artificial isotopes can help explain how elements can change into others through controlled processes.

Neutrons in Nucleus

The nucleus of an atom is composed of two types of subatomic particles: protons and neutrons. Neutrons are critical in stabilizing the nucleus, especially in large atoms with many protons. They act almost like a buffer, offsetting the repulsive forces between positively charged protons.
In the context of the exercise, when analyzing the beta decay process, we see a neutron being converted into a proton. This transformation affects the atomic makeup of the nucleus but not its mass number.

• Mass Number ( A ): The total number of protons and neutrons.
• Atomic Number ( Z ): The number of protons in the nucleus.

Understanding the balance of protons and neutrons within the nucleus is key to determining the stability of an atom and predicting the result of radioactive processes.

Atomic Number

The atomic number, represented as Z , signifies the number of protons within an atom's nucleus. It's a fundamental identifier of an element. Each element on the periodic table is distinguished by its unique atomic number. Changes in this number suggest a transformation from one element to another.
In the given exercise, the atomic number starts at 5 before the process of beta decay and changes to 7. This illustrates the increase by one for each beta decay. The atomic number gives insight into the identity of an element, indicating how many protons are present. Importantly, during beta decay, only the atomic number changes while the mass number remains the same.

Mass Number

The mass number, denoted as A , is the sum of protons and neutrons in an atom's nucleus. It's indicative of the overall size of the nucleus and helps identify isotopes of elements. In the exercise, the focus remains on how the mass number remains unchanged during the process of beta decay, despite changes in the atomic number.
The mass number is calculated by adding the number of protons and neutrons:

• Formula: A = Z + N
• Where Z is the atomic number and N is the number of neutrons.

This exercise demonstrates that despite the transformation happening during beta decay, the mass number remains constant at 14, allowing the identification of the number of neutrons in the parent nucleus before decay.