Question

\({ }_{92} \mathrm{U}^{238}\) is radioactive and it emits \(\alpha\) and \(\beta\) particles to form \({ }_{82} \mathrm{~Pb}^{206} .\) The number of \(\alpha\) and \(\beta\) particles are respectively (a) 8,6 (b) 6,8 (c) 4,2 (d) 8,4

Short answer

Option (a): 8 alpha particles and 6 beta particles.

Step-by-step solution

Identify Alpha Decay Variables

In alpha decay, an unstable nucleus emits an alpha particle, which consists of 2 protons and 2 neutrons. This results in the reduction of the atomic number by 2 and the mass number by 4 for each alpha particle emitted.

Equate Alpha Decay Effects

The original uranium isotope \[{ }_{92} \mathrm{U}^{238} \] decays to \[{ }_{82} \mathrm{Pb}^{206} \].The change in mass number is \ \(238 - 206 = 32\). Each alpha particle decreases the mass number by 4, so \[32 \div 4 = 8\] alpha particles are emitted.

Identify Beta Decay Variables

In beta decay, a neutron decays into a proton, increasing the atomic number by 1. The mass number remains unchanged during beta decay.

Calculate Beta Decay Count

The change in atomic number from uranium to lead is: \[92 - 82 = 10\].Since the emission of 8 alpha particles reduces the atomic number by \(-16\), the actual increment is due to beta decay. Therefore,\[-16 + 10 = -6\],indicating 6 beta particles were emitted.

Key concepts

Alpha Decay

Alpha decay is a common type of radioactive decay where an unstable atomic nucleus emits an alpha particle to become more stable. An alpha particle is made up of two protons and two neutrons, similar to a helium nucleus. This emission reduces the atomic number of the original element by 2 and its mass number by 4.

Through alpha decay, elements find a way to transform themselves into different, more stable elements. For instance, in the process of uranium-238 decaying, the nucleus loses 8 alpha particles to eventually form lead-206. This emission causes a decrease in both atomic and mass numbers each time an alpha particle is released. This reduction is crucial in the steps of radioactive decay pathways and is significant in nuclear physics.

Beta Decay

Beta decay is another form of radioactive transformation where a neutron in the nucleus turns into a proton, thus emitting an electron known as a beta particle. Unlike alpha decay, beta decay increases the atomic number by one while leaving the mass number unchanged.

This process plays a vital role in the decay chain of uranium to lead. After the release of alpha particles in uranium’s decay series, beta decay compensates by increasing the atomic number. In the context of uranium to lead transformation, calculating the increase in the atomic number after beta decay helps in deducing how many beta particles have been emitted, which in the exercise was 6. It shows how both alpha and beta decays work hand-in-hand to convert one element to another over time.

Uranium to Lead Decay

The transformation of uranium-238 to lead-206 is a well-known decay series in radioactive decay processes, involving successive releases of both alpha and beta particles. In this particular pathway, 8 alpha particles are emitted initially, drastically reducing the atomic and mass numbers.

Following this, beta decay comes into play, assisting by regaining lost atomic numbers through the emission of beta particles. Together, these steps sum up the total changes needed to transform uranium into lead. This decay process is an informative example of natural nuclear transformation, providing insights into both the kinetic aspects of radioactivity and the transformation of elements over geological time scales.

Nuclear Transformation

Nuclear transformation refers to the process whereby a particular element changes into another element through nuclear reactions. This includes both natural decay processes, like alpha and beta decays, and artificial transformations in nuclear reactions.

In natural radioactive decay, like the uranium to lead series, this transformation is a series of particle emissions that lead to a completely different and stable element. This transformation is governed by principles of nuclear chemistry and physics, particularly focusing on the stability of atomic nuclei.

Understanding nuclear transformation helps us comprehend the behavior of radioactive substances and predict the longevity and transformations of elements in nature, providing a backbone to several sectors like thermonuclear energy production and radiometric dating techniques.