Question

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

Short answer

(a) an isotope of X

Step-by-step solution

Understanding Alpha and Beta Decay

An alpha particle is a helium nucleus with 2 protons and 2 neutrons. When an element loses an alpha particle, its atomic number decreases by 2 and its mass number decreases by 4. A beta particle is an electron, which results from the decay of a neutron into a proton in the nucleus. When an element loses a beta particle, its atomic number increases by 1 (as a neutron turns into a proton), but its mass number remains unchanged.

Initial Changes after Alpha Decay

Initially, element X loses one alpha particle. This change results in the new atomic number: Z - 2 and the new mass number: A - 4, where Z is the original atomic number and A the original mass number of element X.

Changes after the First Beta Decay

The first beta decay causes the atomic number to increase by 1. So, the new atomic number becomes (Z - 2) + 1 = Z - 1. The mass number stays the same at A - 4.

Changes after the Second Beta Decay

A second beta decay increases the atomic number by another 1, resulting in a final atomic number of (Z - 1) + 1 = Z. The mass number remains unchanged at A - 4.

Comparing Resulting Element with Original

After understanding both types of decay, we compare the new element to the original element X. The new element, after all decays, has an atomic number equal to X but a reduced mass number by 4.

Determining the Relationship

Since the final element has the same atomic number as X but a lower mass number (by 4), it is an isotope of X, as isotopes have the same number of protons but different mass numbers.

Key concepts

Isotopes

Isotopes are fascinating variants of elements where the atoms have the same number of protons in their nucleus but different numbers of neutrons. This means that while the atomic number, which is the count of protons, remains the same, the mass number changes due to the variation in the number of neutrons.

For example, carbon has several isotopes. Carbon-12 and Carbon-14 both have 6 protons (and thus an atomic number of 6) but contain 6 and 8 neutrons respectively. This difference in neutron count is what makes them isotopes.

Isotopes play crucial roles in scientific research and practical applications. From carbon dating in archaeology to medical diagnostic techniques, their utility is vast. In nuclear reactions, such as alpha and beta decay, isotopes may also be formed, varying the mass number while the atomic number stays intact.

Atomic Number

The atomic number, symbolized as Z, is the definitive number that identifies an element. It tells us how many protons are present in the nucleus of an atom. Because protons are positively charged particles, the atomic number also indirectly tells us about the positive charge in the nucleus.

For example, in the exercise you have seen, the element X undergoes radioactive decay. In these processes, while neutrons may change to protons or protons escape the nucleus, the elemental identity of an atom depends on its atomic number.

Even after transformations like beta decay—increasing the atomic number by turning a neutron into a proton—the essence of an element as defined by its protons can remain largely the same. Understanding the atomic number helps comprehend an element’s position on the periodic table and its chemical behaviors.

Mass Number

The mass number, or the nucleon number, represented by A, provides us with the total count of protons and neutrons within an atom's nucleus. It's crucial in determining an atom's isotopic identity. Remember, each isotope of a particular element varies in neutron number, and thus in mass number, while maintaining a consistent proton count.

Consider the alpha decay process. When an element undergoes alpha decay, it loses two protons and two neutrons in the form of an alpha particle. This causes its mass number to decrease by 4—a change that directly impacts the total weight of the nucleus.

Tracking changes in the mass number is essential when analyzing nuclear reactions, ensuring clarity in identifying isotopes and recognizing elemental transformations.

Nuclear Reactions

Nuclear reactions involve processes where changes occur within the atomic nucleus. This differs from chemical reactions, where only the outer electrons in atoms are involved. In nuclear reactions, the focus is on protons and neutrons within the nucleus.

The exercise you encountered highlighted alpha and beta decay, two types of nuclear reactions. In alpha decay, the nucleus ejects an alpha particle (2 protons and 2 neutrons), decreasing both its atomic number and mass number. Beta decay sees a neutron turn into a proton, emitting a beta particle (an electron), thus increasing the atomic number while keeping the mass number stable.

These transformations play essential roles in the stability and transmutation of elements. They affect natural phenomena such as radioactive decay and technological processes in nuclear power and medicine. Understanding nuclear reactions is pivotal in harnessing these powerful processes for human benefit.