Calculating Energy Released in B+ and B- Decay: 14C to 14N and 60Co Max KE

[cashmoney805]

Homework Statement

There are 2 problems

#1. How much energy is released when ¹⁴C decays into ¹⁴N by B emission?

#2. What is the maximum KE of the emitted B particle during the decay of ⁶⁰Co?

Homework Equations

E = (Mass parent - Mass daughter - Mass of B particle?) * 931.5 MeV

The Attempt at a Solution

For question 1, the book did E = (M parent - M daughter)*931.5 MeV = (14.003242 - 14.003074) * 931.5 = .156 MeV

For question 2, the book did KE = (M parent - M daughter - M B particle) * 931.5 = ( 59.933822 - 59.930791 - .000549) * 931.5 = 2.31 MeV

Why did the book not subtract the mass of the B particle in the first and it did subtract the mass of it in the second problem? Thanks for the help

 

[anathema]

!

I can provide some insights into the solutions provided by the book.

For question 1, the book did not subtract the mass of the B particle because it is assumed that the emitted B particle has a negligible mass compared to the parent and daughter nuclei. This assumption is valid for most nuclear decay processes, where the emitted particle has a much smaller mass compared to the parent and daughter nuclei. Therefore, it is not necessary to subtract the mass of the B particle in this case.

For question 2, the book did subtract the mass of the B particle because in this case, the emitted B particle (electron) has a significant mass compared to the parent and daughter nuclei. This is because in the decay of 60Co, the emitted B particle is an electron, which has a mass of approximately 0.000549 amu. Therefore, it is necessary to subtract its mass from the total mass of the parent and daughter nuclei to get the correct value for the maximum kinetic energy of the emitted B particle.

In summary, the mass of the emitted particle should only be subtracted in cases where it has a significant mass compared to the parent and daughter nuclei. In other cases, it can be assumed to have a negligible mass and does not need to be subtracted.

 

[nlightner]

I would like to clarify that the equations used in the book are correct. The difference in the two solutions is due to the different particles involved in the decay process.

In the first problem, the decay is from 14C to 14N by B emission. In this process, a Beta particle (B) is emitted, but it is not necessary to consider its mass in the calculation of energy released. This is because the mass of the Beta particle is very small compared to the mass difference between the parent and daughter nuclei. Therefore, it can be neglected in the equation.

In the second problem, the decay is of 60Co, which involves both B+ and B- emission. The B+ emission results in the emission of a positron (B+) and a neutrino, while the B- emission results in the emission of an electron (B-) and an antineutrino. In this case, the mass of the B particle must be taken into account, as it is a significant contributor to the mass difference between the parent and daughter nuclei.

Overall, the equations used in the book are correct and the difference in the solutions is due to the different decay processes involved. It is important to carefully consider the particles involved in the decay when calculating the energy released.