Problem 140 - A Complete Resource Book in Chemistry for JEE Main

Question

The radio nucliede \({ }_{90}\) Th \(^{234}\) undergoes two successive \(\beta\) decays followed by one \(\alpha\) decay. The atomic number and the mass number respectively of the resulting radio nucliede will be (a) 92 and 234 (b) 94 and 230 (c) 90 and 230 (d) 92 and 230

Step-by-Step Solution

Answer

Option (c): 90 and 230.

Step 1: Understand the Process of Beta Decay

In a beta decay process, a neutron is converted into a proton and an electron (beta particle) is emitted. This increases the atomic number by 1 while the mass number remains unchanged.

Step 2: First Beta Decay

Start with Thorium-234 ( _{90}^{234} ext{Th} ). During the first beta decay, the atomic number increases by 1 (90 to 91), while the mass number remains 234.

Step 3: Second Beta Decay

Apply the second beta decay. The atomic number increases by another 1, going from 91 to 92, while the mass number remains 234.

Step 4: Understand the Process of Alpha Decay

In an alpha decay process, a helium nucleus is emitted. This decreases the atomic number by 2 and the mass number by 4.

Step 5: Alpha Decay

Apply the alpha decay to the resulting nucleus ( _{92}^{234} ext{U} ). The atomic number decreases by 2, resulting in 90, and the mass number decreases by 4, resulting in 230.

Step 6: Conclusion

The resulting radionuclide has an atomic number of 90 and a mass number of 230. So, the answer is option (c), 90 and 230.

Key Concepts

Beta Decay

Beta decay is a fascinating process in nuclear chemistry where a neutron inside the nucleus is transformed into a proton, consequently releasing an electron, known as a beta particle. This transformation affects only the atomic number.

Here are the key points about beta decay:

• The atomic number increases by 1, because a proton replaces a neutron in the nucleus.
• The mass number remains unchanged; it still reflects the total count of protons and neutrons in the nucleus.
• This process emits a small negatively charged beta particle (electron) and a neutrino, which escapes without affecting the nucleus.

In the exercise, when Thorium-234 undergoes beta decay, its atomic number rises from 90 to 91, but its mass number stays at 234. A second beta decay then increases the atomic number to 92 while the mass number remains constant.

Alpha Decay

Alpha decay involves the release of an alpha particle from the nucleus. An alpha particle consists of 2 protons and 2 neutrons, which altogether form a helium nucleus. Let’s break that down:

• The atomic number decreases by 2 due to the loss of 2 protons.
• The mass number decreases by 4, accounting for the 2 protons and 2 neutrons emitted.
• The emitted alpha particle is equivalent to a helium nucleus, making alpha decay significant in decreasing both atomic and mass numbers of the original element.

In the given exercise, following two beta decays, the uranium nucleus resulting from Thorium undergoes alpha decay. This means the atomic number drops from 92 to 90, and the mass number reduces from 234 to 230.

Atomic Number

The atomic number is a fundamental property of an element that tells us how many protons are in the nucleus of an atom. Here’s what you need to remember:

• The atomic number determines the identity of an element. For instance, a change from 90 to 91 indicates a transition from Thorium to Protactinium.
• It changes during nuclear reactions, such as beta and alpha decay, affecting the element but not its isotope properties.
• A higher atomic number generally indicates a heavier element, as it requires a greater number of protons in the nucleus.

In radioactive decay processes, like the example provided, tracking changes in the atomic number helps predict the new element formed after decay events.

Mass Number

The mass number of an atom is the total count of protons and neutrons it possesses. Here's what you should know about it:

• The mass number is represented as the sum of protons (atomic number) and neutrons.
• It provides insight into the isotope of an element, as isotopes vary by their number of neutrons.
• In processes like nuclear decay, the mass number is a telling figure, especially in alpha decay where it decreases due to loss of nuclear particles.

In the exercise's context, while beta decay left the mass number unchanged at 234, alpha decay reduces it by 4, resulting in a final mass number of 230.