Alpha Decay and Total Kinetic Energy

[asifion]

Homework Statement

The polonium isotope 211 Po is radioactive and undergoes alpha decay. In the decay process, a 211 Po nucleus at rest explodes into an alpha particle (a 4 He nucleus) and a 207 Pb lead nucleus. The lead nucleus is found to have 0.12 MeV of kinetic energy. The energy released in a nuclear decay is the total kinetic energy of all the decay products.

How much energy is released, in MeV, in a 211 Po decay?

Relevant Equations

Ei = Ef
K total = K alpha + K Pb

Since we are looking for K total, I summed the given kinetic energy for lead and the typical kinetic energy of an alpha particle: 0.12 + 5 = 5.12 MeV. My answer is definitely wrong, but I don't how I should approach the problem.

 

[PeroK]

Problem Statement: The polonium isotope 211 Po is radioactive and undergoes alpha decay. In the decay process, a 211 Po nucleus at rest explodes into an alpha particle (a 4 He nucleus) and a 207 Pb lead nucleus. The lead nucleus is found to have 0.12 MeV of kinetic energy. The energy released in a nuclear decay is the total kinetic energy of all the decay products.

How much energy is released, in MeV, in a 211 Po decay?
Relevant Equations: Ei = Ef
K total = K alpha + K Pb

Since we are looking for K total, I summed the given kinetic energy for lead and the typical kinetic energy of an alpha particle: 0.12 + 5 = 5.12 MeV. My answer is definitely wrong, but I don't how I should approach the problem.

Have you thought about what quantity must be conserved in a decay?

 

[asifion]

Energy? Not quite sure what you are getting at. I was thinking Ui + Ki = Uf + Kf where Ki is 0.

 

[PeroK]

Energy? Not quite sure what you are getting at. I was thinking Ui + Ki = Uf + Kf where Ki is 0.

Not energy. Hint: Newton's third law.

 

[asifion]

Force?

 

[PeroK]

Force?

One thing you must never forget is conservation of momentum.

 

[asifion]

But we aren't given any velocity

 

[PeroK]

But we aren't given any velocity

It depends what you mean by "given". You are given the KE and you can look up the mass of the components.

You need to think how KE relates to momentum.

 

[asifion]

KE = p^2 / 2m

 

[PeroK]

KE = p^2 / 2m

Good. You need to look at how to solve the problem now. I'm going offline now, but maybe someone else can help if needed.

 

[asifion]

Thanks for the help; I figured it out.