Chapter 31: Problem 23
$$ \text { Find the energy (in MeV) released when } \alpha \text { decay converts radium } $$ \(\frac{226}{88} \mathrm{Ra}\) (atomic mass \(\left.=226.02540 \mathrm{u}\right)\) into radon \({ }_{86}^{222} \mathrm{Rn}\) (atomic mass \(=\) \(222.01757 \mathrm{u}) .\) The atomic mass of an \(\alpha\) particle is \(4.002603 \mathrm{u}\).
Short Answer
Step by step solution
Understanding the Problem
Identifying Mass Defect
Calculate Mass Defect
Convert Mass Defect to Energy
Calculate Energy Released
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mass Defect
The principle is based on Einstein's mass-energy equivalence formula, where the 'missing' mass is converted into energy. Hence, the mass defect is directly related to the energy released in nuclear reactions like alpha decay.
- Calculate the mass defect by subtracting the total mass of the decay products from the original nucleus mass.
- This mass defect translates to energy through the formula: \( E = \Delta m \times c^2 \) where \( c \) is the speed of light.
- In practical calculations, the mass defect in atomic mass units (u) is converted to energy (MeV) using the factor 931.5 MeV/u.
Radium-226
Alpha particles are essentially helium nuclei, consisting of two protons and two neutrons. During the alpha decay of radium-226:
- The nucleus releases an alpha particle and turns into radon-222.
- This decay leads to a decrease in the atomic number by two and the mass number by four.
- The emission results in a significant amount of energy release, which is characteristic of such radioactive decays.
Radon-222
In the decay process:
- Radon-222 emerges as a result of radium-226 losing an alpha particle.
- This new element is still radioactive and continues to decay in a sequence of further decay reactions until it finally becomes a stable lead isotope.
- Since radon-222 is a gas, it can escape into the atmosphere, posing health risks if accumulated in enclosed spaces.
Nuclear Physics
Key areas in nuclear physics related to alpha decay and energy release include:
- Understanding the interactions within the nucleus which dictate why certain elements undergo alpha decay.
- Applying mass-energy equivalence to calculate energy release, vital for power generation and nuclear medicine.
- Exploring the principles behind nuclear stability and the factors influencing decay rates.