Understanding Beta-decay: Differentiating Mass Deficit and Mass Excess

[trv]

Trying to study Beta-decay, but can't seem to be able to tell the difference between the two. Can someone help?



Edit: I get Mass deficit. Still don't quite get mass excess.

 

[Bob S]

Beta decay occurs when there is a mass excess of more than the mass of the electron. One example is the beta decay of the neutron to a proton plus an electron and a neutrino. The neurton's mass is (Mc^2) 939.565 MeV, proton mass 938.272 meV, and electron mass 0.511 MeV, so the excess mass is 1.293 MeV.

 

[trv]

Hi Bob thanks for the reply. My question however was more on mass excess itself. I'm sure its a pretty simple concept. Can't quite get my head around it however.

I do have the definition
Mass Excess=M(Z,A)(in amu) - A.

I can't quite tell the difference between the two terms on the right. They seem the same to me.

Is the following correct?

A=no. of nucleons*(mass of nucleon)
Mass of nucleon=average(proton,neutron)

The M(Z,A) then actually considers that protons and neutrons have different masses, and also binding energies and we get a slightly different value.

Edit:Corrected mistake in formula.

 

[Bob S]

trv-
I do not know exactly what you mean by M(Z,A) on both the left hand and right hand side. But let's consider one isotope, lead 206, and see how AMUs work out.

Mass Pb 206 === 205.974 AMU

82 protons @ 1.007276 = 82.597 AMU

124 neutrons 1.008665 = 125.074
---------
Sum of 124 n and 82 p === 207.671 AMU

Difference === -1.697 AMU

How do these relate to your formula?

 

[trv]

OK firstly, your right, the M(Z,A) was a typo and has been corrected. Now here's how I'd relate those values...

Mass Deficit= -1.697 AMU
M(Z,A)=205.974 AMU
A=207.671

Is this correct?

But then I'm a little confused by how it differs from the mass deficit. The formula I have goes as follows,

Mass deficit=M(Z,A)-Z(M_p+m_e)-NM_n

Is it just that one considers only the nucleus and the other an atom as a whole, including the electrons? Also wouldn't both have negative values so why is one called an excess and the other a deficit? Other possibility is just that one is the negative of the other, but looking at the formulae, that doesn't seem likely.

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Alternatively,
Mass excess=205.974-206=-0.26
Mass deficit=205.974-207.671-M_e=-1.697-M_e

 

[Bob S]

You are correct in also including the electron mass. To be exact, you probably need to include the sum of all electron binding energies, which could easily amount to another electron mass. Here is a wiki website giving mass details for the deuteron, including atomic mass, binding energy and excess energy, which can be analyzed to include the electron mass, neutron mass and neutron mass.
http://en.wikipedia.org/wiki/Deuterium

 

[trv]

Get it, thanks for the help BOB.