# Mass deficit and mass excess

• trv
In summary, Beta decay occurs when there is a mass excess of more than the mass of the electron. The mass excess is 1.293 MeV for the beta decay of the neutron to a proton plus an electron and a neutrino.

#### 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.

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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.

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.

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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?

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(Mp+me)-NMn

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-Me=-1.697-Me

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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

Get it, thanks for the help BOB.

## 1. What is mass deficit and mass excess?

Mass deficit and mass excess are two important concepts in physics that describe the difference between the measured mass and the calculated mass of a system. Mass deficit refers to the difference between the measured mass and the sum of the individual masses of the constituent particles, while mass excess refers to the difference between the measured mass and the mass of the most stable isotope of the element.

## 2. Why do mass deficit and mass excess occur?

Mass deficit and mass excess occur due to the conversion of mass into energy, as described by Einstein's famous equation E=mc^2. This means that when particles combine or split, they release or absorb energy, which results in a difference between the measured mass and the calculated mass of the system.

## 3. How are mass deficit and mass excess measured?

Mass deficit and mass excess can be measured using various scientific techniques, such as mass spectrometry, nuclear reactions, and nuclear decay. These methods involve measuring the masses of particles before and after a reaction or decay, and calculating the difference between them.

## 4. What are the practical applications of understanding mass deficit and mass excess?

Understanding mass deficit and mass excess is crucial in many fields of physics, such as nuclear physics, astrophysics, and nuclear medicine. These concepts help us understand the stability and composition of atoms, the energy released in nuclear reactions, and the properties of nuclear fission and fusion. They also have practical applications in medical imaging and cancer treatment.

## 5. Can mass deficit and mass excess be negative?

Yes, mass deficit and mass excess can be negative. This means that the measured mass is less than the calculated mass, indicating that the system has a deficit of mass or excess of energy. This is common in nuclear reactions, where the released energy can result in a decrease in the measured mass of the system.