Problem 26 - A Complete Resource Book in Chemistry for JEE Main

Question

In successive emission of \(\beta\) and \(\alpha\) particles, how many \(\alpha\) and \(\beta\) particles should be emitted for the natural \(\left(4 \mathrm{n}+1\right.\) series) conversion of \({ }_{94} \mathrm{Pu}^{241}\) to \({ }_{92} \mathrm{U}^{233}\) ? (a) \(2 \alpha, \beta\) (b) \(2 \alpha, 2 \beta\) (c) \(2 \alpha, 3 \beta\) (d) \(\alpha, 2 \beta\)

Step-by-Step Solution

Answer

Option (b): 2 \(\alpha\), 2 \(\beta\).

Step 1: Understand Alpha and Beta Decay

In alpha decay, the emitting nucleus loses 2 protons and 2 neutrons, reducing its atomic number ( Z) by 2 and mass number ( A) by 4. In beta decay, a neutron is converted to a proton, increasing the atomic number by 1 but keeping the mass number the same.

Step 2: Calculate Total Changes Needed

The original nucleus is _{94} Pu^{241} and the target nucleus is _{92} U^{233}. The changes needed are a reduction in atomic number by 2 (from 94 to 92) and in mass number by 8 (from 241 to 233).

Step 3: Determine the Number of Alpha Particles

Each alpha particle emission changes the atomic number by -2 and the mass number by -4. To decrease the mass number by 8, 2 alpha particles must be emitted since each reduces the mass number by 4 (8/4 = 2).

Step 4: Determine the Number of Beta Particles

Each beta particle emission increases the atomic number by 1. After emitting 2 alpha particles, the atomic number is reduced to 90 (94 - 2*2 = 90). To reach an atomic number of 92, 2 beta particles must be emitted (90 + 2 = 92).

Step 5: Conclusion from Steps

The emission sequence requires 2 alpha particles and 2 beta particles, aligning with option (b).

Key Concepts

Alpha Decay

One of the fundamental processes in nuclear decay is alpha decay. In this process, the nucleus of an atom releases an alpha particle composed of 2 protons and 2 neutrons. This results in the reduction of:

• Atomic number by 2, because it loses 2 protons.
• Mass number by 4, due to the loss of protons and neutrons.

Alpha decay is common in heavy elements where this emission helps the nucleus reach a more stable state.
For example, when an alpha particle is emitted from \(_{94}^{241}\text{Pu}\), it transforms into a new element, with a decreased atomic and mass number.

Beta Decay

Beta decay is another vital nuclear process. Unlike alpha decay, beta decay involves the transformation of a neutron into a proton, alongside the emission of an electron, referred to as a beta particle.

• Increases the atomic number by 1, due to the conversion of a neutron into a proton.
• No change to the mass number, as the number of nucleons (protons + neutrons) remains unchanged.

This decay process aids in adjusting the neutron-to-proton ratio in the nucleus to enhance stability.
For instance, through beta decay, the product of alpha decay poisons further reaction processes, such as transforming \(_{90}^{233}\text{Th}\) into \(_{91}^{233}\text{Pa}\).

Radioactive Series

Nuclear decay chains or radioactive series are sequences of successive transformations.
They detail how unstable isotopes transform into more stable forms by emitting particles like alpha and beta particles. These series start with a parent isotope and follow decay products to the final stable isotope.
The 4n+1 series is one specific type of these decay chains, which:

• Begins with \{_\alpha\}, triggering multiple decays until stability is achieved.
• Shows how specific isotopes decay in a sequence, such as the conversion of \(_{94}^{241}\text{Pu}\) to \(_{92}^{233}\text{U}\) through combined alpha and beta emissions.

Pu-241

_Pu-241_, or Plutonium-241, is an isotope of plutonium characterized by many prominent properties. Critical in the 4n+1 radioactive series, this isotope plays a significant role in nuclear science applications, particularly energy generation and weaponry.

• With a mass number of 241, _Pu-241_ is a potent source of alpha particles.
• Its decay ultimately leads to the formation of Uranium-233 through a series of emissions.
• Importantly, each decay step of _Pu-241_ results in significant changes such as the emission of alpha particles, reducing atomic and mass numbers, facilitating the transition to more stable configurations.

U-233

Uranium-233, denoted as _U-233_, serves as the endpoint in the decay chain of \(_{94}^{241}\text{Pu}\) through a series of nuclear transformations.

• It is reached through successive emissions of both alpha and beta particles.
• _U-233_ is significant as a potential fuel in nuclear reactors due to its fissile nature.

This isotope is notable in energy research and industrial applications.
As _U-233_ emerges from the decay of heavier isotopes via radioactive series like the 4n+1 chain, it exemplifies the intricate pathways of nuclear transformation leading to more stable, usable forms.