Q-Value | KE of Alpha Decay (Kinematics)

Introduction to Nuclear Decay

In this section, we learn about the instability of nuclei and the process of radioactive decay. We explore how larger nuclei undergo alpha decay to become more stable.

Nucleus Instability and Radioactive Decay

• Nuclei are unstable when short-range nuclear forces cannot dominate over coulombic repulsion.

• When a nucleus becomes too large (mass number > 210), it undergoes radioactive decay.

• Alpha decay is a spontaneous process where a nucleus emits an alpha particle, reducing its size and becoming more stable.

• The emitted energy in this process is known as the disintegration energy or Q value of the reaction.

Calculating Q Value of a Reaction

• The Q value of a reaction can be calculated by looking at the masses of the parent and daughter nuclei.

• Energy released in nuclear reactions is manifested as mass energy, which gets converted into disintegration energy.

• In alpha decay, the mass of the parent nucleus minus the mass of both daughter nuclei gives the mass defect, which is proportional to the disintegration energy.

Expressing Disintegration Energy

• Disintegration energy can be expressed as kinetic energy of the alpha particle and kinetic energy of the daughter nuclei.

• Conservation laws for linear momentum and energy can be applied to calculate these energies.

• The ratio of masses can be written as a ratio of mass numbers since neutrons and protons have approximately equal masses.

Kinetic Energy Calculation in Alpha Decay

This section focuses on calculating the kinetic energy distribution between an alpha particle and daughter nuclei during alpha decay.

Conservation Laws in Alpha Decay

• Conservation laws for linear momentum and energy can be applied to analyze alpha decay.

• Momentum conservation states that momentum before decay equals momentum after decay for two particles involved.

• Energy conservation states that the energy released in the reaction is distributed as kinetic energy of the alpha particle and daughter nuclei.

Kinetic Energy Calculation

• The kinetic energy of the alpha particle can be calculated using the mass ratio and Q value of the nuclear reaction.

• The ratio of masses can be expressed as a ratio of mass numbers since neutrons and protons have approximately equal masses.

• The kinetic energy of the alpha particle is equal to M/(M + M_alpha) multiplied by the Q value.

Summary and Conclusion

This section summarizes the key points discussed in the transcript regarding nuclear decay and calculating disintegration energy.

Key Points

• Nuclei become unstable when short-range nuclear forces cannot dominate over coulombic repulsion.

• Larger nuclei undergo alpha decay, emitting an alpha particle to become more stable.

• The disintegration energy or Q value of a reaction can be calculated using mass defects and conservation laws for momentum and energy.

• Conservation laws help determine how much disintegration energy is distributed as kinetic energy between an alpha particle and daughter nuclei.

Expression for Kinetic Energy of Alpha Particle

In this section, the expression for the kinetic energy of an alpha particle in an alpha decay process is derived. The mass number (a), Q value, and disintegration energy are used to calculate the total amount of kinetic energy carried off by the alpha particle.

Derivation of the Expression

• The expression for the kinetic energy of the alpha particle is given by:

• Kinetic Energy = (Mass Number (a) - 4) / a * Q Value

• This equation represents the total amount of kinetic energy carried off by the alpha particle from the available disintegration energy.

Example Calculation

• An example of an alpha decay process is provided using uranium-238 decaying into thorium-234.

• The total amount of energy released in this specific example is approximately 5.30 mega electron volts (MeV).

• By calculating from the expression, it can be determined that around 98.3% of this energy goes off as kinetic energy of the alpha particle.

• Therefore, in this case, approximately 98.3% of the Q value (around 5.2 MeV) represents the amount of energy carried off as kinetic energy by the alpha particle.

Majority of disintegration energy in an alpha decay process usually goes off as kinetic energy of the alpha particle.

Alpha Decay Process and Energy Distribution

This section discusses an example of an alpha decay process involving uranium-238 and thorium-234. It highlights how a significant portion of disintegration energy is typically released as kinetic energy carried by the alpha particle.

Example Calculation Continued

• In our example with uranium-238 decaying into thorium-234:

• Mass number (a) of the parent nucleus (uranium-238) is 238.

• Mass number (a - 4) of the daughter nucleus (thorium-234) is 234.

• By substituting these values into the expression, it can be calculated that approximately 98.3% of the Q value represents the kinetic energy carried off by the alpha particle.

The specific example demonstrates that a large percentage of disintegration energy in an alpha decay process goes off as kinetic energy of the alpha particle.