Problem 146 - A Complete Resource Book in Chemistry for JEE Main

Question

In the transformation of \(_{92} \mathrm{U}^{238}\) to \({ }_{92} \mathrm{U}^{234}\), if one emission is an \(\alpha\) particle, what should be the other emission(s)? \([2006]\) (a) two \(\beta\) (b) two \(\beta^{-}\)and one \(\beta^{+}\) (c) one \(\beta\) - and one \(\gamma\) (d) one \(\beta^{-}\)and one \(\beta^{-}\)

Step-by-Step Solution

Answer

Option (a): two \(\beta\) emissions.

Step 1: Understand the Alpha Decay

An \(\alpha\) particle consists of two protons and two neutrons, which is equivalent to a helium nucleus \(^{4}_{2}\text{He}\). When \(^{238}_{92}\mathrm{U}\) undergoes \(\alpha\) decay, it loses two protons and two neutrons, resulting in \(^{234}_{90}\text{Th}\).

Step 2: Identify the Outcome of Alpha Decay

After the emission of the \(\alpha\) particle, the uranium transforms to thorium, \(^{234}_{90}\mathrm{Th}\). This is because the emission of an \(\alpha\) particle reduces the atomic number by 2 and the mass number by 4.

Step 3: Analyze the Remaining Change

The final product is \(^{234}_{92}\mathrm{U}\). As we initially transformed into \(^{234}_{90}\text{Th}\) after the \(\alpha\) decay, an increase in the atomic number by 2 is needed. This suggests two \(\beta^{-}\) emissions, as each \(\beta^{-}\) emission increases the atomic number by 1 while keeping the mass number the same.

Step 4: Verify the Emissions

Confirm that two \(\beta^{-}\) emissions convert \(^{234}_{90}\text{Th}\) back to \(^{234}_{92}\mathrm{U}\). With each \(\beta^{-}\) emission, a neutron converts into a proton, hence increasing the atomic number by 1 for each \(\beta^{-}\) emission.

Key Concepts

Alpha Decay

Alpha decay is a type of nuclear decay where an atomic nucleus emits an alpha particle. An alpha particle is essentially a helium nucleus, consisting of two protons and two neutrons. When an atom undergoes alpha decay, the mass number decreases by 4 because it loses both the two protons and two neutrons.
As a result, the atomic number decreases by 2, which means the element changes into a different one, positioned two places backward on the periodic table.
Alpha decay is common in heavy elements, where the strong nuclear force isn't enough to hold the nucleus together tightly. Since it decreases the mass number significantly, it's an important process in understanding radioactive decay chains. Although alpha particles are large, they are not very penetrating and can be stopped by a sheet of paper or human skin.

Beta Decay

Beta decay transforms a neutron into a proton or vice versa, with the emission of a beta particle. There are two types of beta decay: beta-minus (β⁻) and beta-plus (β⁺) decay.

• **Beta-minus (β⁻) decay**: This occurs when a neutron in the nucleus converts into a proton, with the emission of an electron (the beta particle) and an anti-neutrino. Each β⁻ decay increases the atomic number by 1 while keeping the mass number unchanged, effectively moving the element one place forward in the periodic table.
• **Beta-plus (β⁺) decay**: This process involves a proton converting into a neutron, accompanied by the release of a positron (the beta-plus particle) and a neutrino. Here, the atomic number decreases by 1, decreasing the number of protons without changing the mass number.

Beta particles are smaller than alpha particles and can penetrate materials more deeply, requiring plastic or glass to be stopped.

Atomic Number

The atomic number is a fundamental property of an element, representing the number of protons in the nucleus of its atoms. This number uniquely identifies an element and determines its position in the periodic table. For example, uranium has an atomic number of 92 because it contains 92 protons in its nucleus.
The atomic number is crucial in nuclear reactions, such as decay processes, because it dictates how an element transforms during these reactions. In alpha decay, the atomic number decreases by 2, while in beta-minus decay, it increases by 1. Understanding the atomic number helps predict the new element that forms after decay.

Mass Number

The mass number, also known as the nucleon number, indicates the total number of protons and neutrons in an atom’s nucleus. It provides insight into the isotope form of an element. For example, the isotope Uranium-238 has a mass number of 238, with 92 protons and 146 neutrons.
In nuclear reactions, such as alpha and beta decay, the mass number plays a key role in identifying isotopes and predicting products of decay. During alpha decay, the mass number decreases by four as two protons and two neutrons are ejected in the form of an alpha particle. In beta decay, the mass number remains unchanged because the transformation involves converting a neutron to a proton or vice versa. Understanding the mass number allows students to balance nuclear equations accurately, providing clarity to otherwise complex transformations in decay processes.