Problem 48 - A Complete Resource Book in Chemistry for JEE Main

Question

If uranium (mass number 238 and atomic number 92 ) emits an \(\alpha\) particle, the product has mass number and atomic number (a) 234 and 90 (b) 236 and 92 (c) 238 and 90 (d) 236 and 90

Step-by-Step Solution

Answer

The product has mass number 234 and atomic number 90.

Step 1: Understanding Alpha Decay

In alpha decay, an atomic nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This means the atomic number of the original nucleus decreases by 2, and the mass number decreases by 4.

Step 2: Initial Uranium Atom

The initial uranium atom we are considering has a mass number of 238 and an atomic number of 92. This is written as \( ^{238}_{92}\text{U} \).

Step 3: Applying Alpha Decay

After emitting an alpha particle (2 protons and 2 neutrons), the mass number of the uranium nucleus decreases from 238 to \(238 - 4 = 234\), and the atomic number decreases from 92 to \(92 - 2 = 90\).

Step 4: Determine the Product

The product of the alpha decay will have a mass number of 234 and an atomic number of 90, written as \( ^{234}_{90}\text{Th} \). This corresponds to option (a) given in the problem.

Key Concepts

Isotopes

Isotopes are atoms of the same element that have the same number of protons but differ in the number of neutrons. This means isotopes have the same atomic number, but different mass numbers. For example, carbon can have isotopes with 6 protons, but varying neutrons like carbon-12, carbon-13, and carbon-14.
Isotopes are important in nuclear chemistry since they can exhibit different stability. Some isotopes are stable, while others are radioactive and can undergo nuclear reactions like alpha decay. This process changes the isotope's composition, creating a different element entirely.

Nuclear Reactions

Nuclear reactions involve changes to an atom's nucleus and can result in the transformation of one element into another. This distinguishes them from chemical reactions, where only the electrons are rearranged.
A key type of nuclear reaction is alpha decay, where an unstable nucleus emits an alpha particle to become more stable. This release causes changes in both the atomic number and mass number of the element. In our exercise, uranium undergoes alpha decay, changing into thorium by emitting an alpha particle (2 protons and 2 neutrons).

Mass Number

The mass number of an atom is the total number of protons and neutrons in its nucleus. Since protons and neutrons make up nearly all of an atom's mass, the mass number is key in identifying isotopes.
For uranium in the exercise, the mass number is initially 238. During alpha decay, 4 nucleons are emitted, reducing the mass number by 4, resulting in a product with a mass number of 234. Mass number dictates the identity and mass of the element, crucial for nuclear reactions.

Atomic Number

The atomic number of an element is the number of protons in its nucleus. It determines the identity of the element and remains constant for isotopes of the same element. Unlike mass number, which can change, the atomic number is fixed for each element.
In an alpha decay, as seen in uranium's decay to thorium, the atomic number decreases by 2 because 2 protons are lost. This decrease changes the element to a different one on the periodic table, making atomic number a fundamental component in nuclear reactions.