Question

An element X loses one \(\alpha\) and two two \(\beta\) particles in three successive stages. The resulting elements will be (a) an isotope of \(\mathrm{X}\) (b) an isobar of \(X\) (c) an isotone of \(X\) (d) X itself

Short answer

(a) The resulting element will be an isotope of X.

Step-by-step solution

Understand Alpha Decay

An \( \alpha \) particle consists of 2 protons and 2 neutrons, which means a total loss of 4 nucleons when an atom undergoes \( \alpha \) decay. This decreases the atomic number by 2 and the mass number by 4.

Apply Alpha Decay to Element X

When element X loses one \( \alpha \) particle, its atomic number decreases by 2 and the mass number decreases by 4. If \( \text{X} \) originally has an atomic number \( Z \) and a mass number \( A \), the new element, let's call it \( Y \), will have atomic number \( Z-2 \) and mass number \( A-4 \).

Understand Beta Decay

A \( \beta \)-particle emission (\( \beta^- \) decay) involves the conversion of a neutron into a proton, thus increasing the atomic number by 1 while the mass number stays constant.

Apply Beta Decay to Element Y

After the first \( \beta \) decay, element Y (\( Z-2 \), \( A-4 \)) will gain 1 proton, becoming \( (Z-1, A-4) \). After the second \( \beta \) decay, the atomic number increases by another 1, resulting in \( Z, A-4 \).

Identify the Resulting Element Characteristics

After going through one \( \alpha \)-decay and two \( \beta \)-decays, the resulting element has an atomic number equal to the original element and a mass number that is 4 less. Thus, the resulting element is an isotope of X, since isotopes have the same atomic number but different mass numbers.

Key concepts

Alpha Decay

When an atom undergoes alpha decay, it emits an alpha particle. An alpha particle consists of 2 protons and 2 neutrons. This means that the atom loses a total of 4 nucleons.
This decay decreases the atomic number by 2, as it loses two protons. Additionally, it reduces the mass number by 4, accounting for both the protons and neutrons lost.
Alpha decay typically occurs in heavy elements where the balance of energy makes it favorable for the nucleus to shed these nucleons.

Beta Decay

Beta decay involves the transformation of a neutron in the nucleus into a proton. During this process, a beta particle (or electron) is emitted from the atom.
There are two main types of beta decay: beta-minus (b2^-) decay and beta-plus (b2^+) decay. In beta-minus decay, a neutron becomes a proton, increasing the atomic number by 1 while keeping the mass number constant.
In contrast, beta-plus decay turns a proton into a neutron, decreasing the atomic number by 1. Beta decay helps the nucleus achieve greater stability by altering the neutron-to-proton ratio.

Isotopes

Isotopes are different forms of the same element. They share the same atomic number but have different mass numbers.
Having the same atomic number indicates that isotopes share the same number of protons and place in the periodic table. But, they contain different numbers of neutrons, leading to varying mass numbers.
This variance can affect the physical and some chemical properties of the isotopes, such as nuclear stability, leading to some isotopes being stable and others radioactive.

Atomic Number

The atomic number is a crucial characteristic of an element. It represents the number of protons in an atom's nucleus.
This number defines the identity of the element and determines the position of the element in the periodic table.
Since elements are defined by their number of protons, the atomic number is what distinguishes one element from another. Changes in the atomic number can transform one element into another, which frequently occurs in nuclear reactions.

Mass Number

The mass number of an element is the total number of protons and neutrons in the nucleus of an atom.
While the atomic number is limited to counting protons, the mass number counts all nucleons, making it a broader measure of the atom's core composition.
The mass number is crucial in distinguishing isotopes, as variations in the number of neutrons result in different mass numbers for isotopes of the same element.