Radium- 226 decays as 88^226 Ra → 86^222 Rn+ 2^4 He . If the 88^226 Ra nucleus is at rest befo

step 1 In this question, we want to find the kinetic energy that was taken by the alpha particle in the

Radium- 226 decays as 88^226 Ra → 86^222 Rn+ 2^4 He . If...

Radium- 226 decays as ${ }_{88}^{226} \mathrm{Ra} \rightarrow{ }_{86}^{222} \mathrm{Rn}+{ }_{2}^{4} \mathrm{He} .$ If the ${ }_{88}^{226}$ Ra nucleus is at rest before the decay and the ${ }_{86}^{222} \mathrm{Rn}$ nucleus is in its ground state, estimate the kinetic energy of the $\alpha$ particle. (Assume that the ${ }_{86}^{222} \mathrm{Rn}$ nucleus takes away an insignificant fraction of the kinetic energy.)

Key Concepts

Conservation of Energy and Momentum

In any decay process, both energy and momentum must be conserved. During nuclear decay, the energy released (the Q-value) is distributed among the decay products in such a way that the momentum balance is maintained. When one product is significantly heavier than the other, it takes away a comparatively small amount of kinetic energy, allowing for an approximation where the lighter particle receives most of the energy.

Kinetic Energy Distribution in Nuclear Decay

Estimating the kinetic energy of decay products involves understanding that the lighter emitted particle typically acquires most of the available energy. This is due to energy and momentum conservation principles and the effect of the mass ratio between the products. In scenarios where one product’s mass is much larger, its kinetic energy contribution is minimal, simplifying the analysis of the energy imparted to the lighter particle.

Alpha Decay

Alpha decay is a nuclear process in which an unstable nucleus emits an alpha particle, a bundle of two protons and two neutrons. This type of decay reduces the parent nucleus’s atomic number by two and its mass number by four. It is a common mode of radioactive decay in heavy elements and is important for understanding how excess nuclear mass is shed to achieve greater stability.

Q-value and Mass Defect

The Q-value of a nuclear reaction represents the energy released during the decay, arising from the mass defect—the difference in mass between the initial nucleus and the final decay products. Through the principle of mass-energy equivalence (E = mc²), this missing mass is converted into kinetic energy, providing a method to estimate the energy available to the emitted particles.

Transcript

Please give Ace some feedback