Calculating Average Binding Energy per Nucleon and Decay of Free Neutrons

[SteveoFitz]

Hey guys, simple question about binding energy. I'm asked to find the average binding energy per nucleon of Magnesium-26. Now I thought that I would have to use: Binding E = (Zmp + Nmn - Ma) X 931.494 MeV/u. Where Z is the atomic #, N is the # of neutrons, mp, mn, and Ma are mass of proton, mass of neutron, and mass of nucleus respectively. My question is for Ma would that just be the atomic weight of the atom since it's asking for average binding energy?

Actually I got one more on nuclear physics as well. The questions asks: Free neutrons have a characteristic half-life of 10.4 min. What fraction of a group of free neutrons with kinetic energy 0.0414 eV will decay before traveling a distance of 12.2 km? Do not enter unit. I don't know where to start on this one, we're not given a relationship between these quantities so I'm assuming there's something I'm supposed to interpret from this data.

Anyways, hopefully someone can help thanks!
Steve

 

[cookiemonster]

For the second one, you need to use special relativity. From the energy of the neutron, you can calculate the velocity and thereby the time dilation. Then you just need to figure out how long the neutron takes to travel the 12.2km in its own reference frame.

Edit: Actually, those numbers seem small enough you might not need to use special relativity. If you haven't learned it, don't try to. Just calculate the velocity based on the given kinetic energy.

cookiemonster

 

[SteveoFitz]

I'm still having problems on this second one, sure i can get the velocity, and then the time using the 12.2 km. However then how am I supposed to find the fraction of neutrons from this data, I'm still perplexed to say the least.

 

[kuengb]

The decay is exponential: If you have N neutrons at t=0, N(t)=N*e^{-const*t}.

Find the constant to get the correct half-life (meaning: after t_{half} there are 50% of the Neutrons left), and then put in the time you found.

I don't think you have to use SRT here, 0.0414eV is not so much