What is Mass defect: Definition and 42 Discussions

Nuclear binding energy is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons attracted to each other by the strong nuclear force.
The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, E=mc2, where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass, This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse (nuclear fusion), or when heavy nuclei split (nuclear fission), either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power, or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles (nuclear fission products).
These nuclear binding energies and forces are on the order of one million times greater than the electron binding energies of light atoms like hydrogen.

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  1. P

    I Energy released calculation using Binding energy and mass defect

    Consider the equation X (200, 50) + n (1, 0) -> Y (120, 30) + Z (70, 20) + 11 n(1, 0) Let p be the mass of a proton, n be the mass of a neutron. BE(X) = [50p + 150n - M(X)] c^2 BE(Y) = [30p + 90n - M(Y)] c^2 BE(Z) = [20p + 50n - M(Z)]c^2 The energy released when using BE (products) - BE...
  2. A

    B Mass Defect: Is my understanding correct?

    Mass – Energy Relationship: According to Einstein’s special theory of relativity, when the energy of a body increases, so does its mass, and vice versa. If the difference in energy is indicated by ΔE and the difference in mass by Δm, these two quantities are related by his famous equation...
  3. A

    Calculate the mass defect of a carbon-12 nucleus

    My attempt: Proton 1.00728ux6+ Neutron 1.00866ux6=12.09564u 12.09564u-11.9967u=0.09894u E=mc^2 E=0.09894x(3.00x10^8ms-^1)^2
  4. K

    B What causes mass defect in the nucleus?

    Hi. I read that the mass of nucleons in nucleus of Oxygen-16 (or nucleus of another atom) is less than the sum of its nucleons if they were separated (also the mass of 8 protons and 8 neutrons). But why does nucleons have less energy in nucleus of atoms than if they were separated? What causes...
  5. Candidus

    I Why does a Mass Defect Exist if |PE| Increases?

    Hello. Can you shed a different light on why mass defects exist please, so that I might finally grasp it intuitively?! I've had a look at these nuclear threads and one about GPE, https://www.physicsforums.com/threads/why-is-there-a-mass-defect-in-the-nucleous.374443/...
  6. A

    I Is the mass defect still considered with invariant mass?

    Hello. Suppose you were to assemble a sphere of negative charges. When you are done, the rest mass of the sphere is larger than that of the negative charges because they gain energy in forming the sphere. But the invariant mass of the electrons can't change and apparently gaining energy doesn't...
  7. I

    I Mass Defect: Exploring the Possibilities of Quantum Mechanics

    I've just watched a video by PBS spacetime on how an object with more potential energy has more mass, or less, in some cases (mass defect). But there is a problem. Quantum mechanics tells us that a particle has a chance of appearing at difderent places ( wave function), and that it also...
  8. C

    I Beta decay and mass defect

    Hi, I was reading the wiki article here on beta decay and energy release: https://en.wikipedia.org/wiki/Beta_decay#Energy_release In obtaining a condition on the masses of the initial and final atoms we neglected the difference in electron binding energies of the two atoms. Does this mean we...
  9. Anonymous Vegetable

    What is the reason for mass defect in a nuclide?

    I may be misguided here but to my understanding, separate nucleons have a higher mass altogether than the combined nucleus as the potential energy gained from being separated (in the field of the strong force) is being manifested in more mass. If this is true, and if it's not I'd like to know...
  10. N

    Gravitational mass defect

    Hello, in nuclear physics we have a mass defect by the binding energy of the nuclides. A similar effect appears in the theory of gravitation induced by the gravitational binding energy, which reduces the mass. But for example at the ISCO of an Kerr black hole we have binding energys about...
  11. I

    Understanding Mass Defect: Energy Calculation in Fusion and Fission

    Hi, this may be a very trivial question but, When calculating energy, is it BE(products) - BE(reactants) or is it the other way round? I have been solving questions and the solutions were products - reactants for some and reactants - products for some. Also for mass defect , is it mass (...
  12. B

    Proton-proton I chain and mass defect reactants and products

    Hello there, I'm starting S382 astrophysics with the OU. The course book says "The proton-proton chain converts four hydrogen nuclei (protons) into a ^4_2He nucleus, two positrons that quickly collide with electrons and are annihilated, and two neutrinos. Hence, branch I of the p-p chain may be...
  13. D

    Mass defect of hydrogen atom

    What's the mass difference between a hydrogen atom and it's constituent particles when they are free, I'm talking about the proton and the electron, not the quarks that make up the proton.
  14. B

    Mass defect and binding energy

    Homework Statement The difference between the mass of one oxygen atom and the sum of the masses of its parts is approx. 2.27 x 10^-28 kg. What is the binding energy that holds an oxygen atom together? (The charge on one electron is 1.6x10^-19 C). Homework Equations E = mc^2 The Attempt at a...
  15. R

    How to relate mass defect to kinetic energies?

    Homework Statement Just one more nuclear question if I may, Homework Equations None. The Attempt at a Solution I can do the first part of this question, but am unsure on the second part. I thought it may be related to the Q-factor (the difference in energy of the initial and final products...
  16. D

    Calculating Mass Defect of Americium-244

    Homework Statement Americium-244 is a rare isotope of Americium. What is the mass defect of Americium-244? Use the following values for atomic and neutron masses when calculating your answer: Homework EquationsThe Attempt at a Solution This was what I did: Mass of protons = 95 x...
  17. K

    Calculate the mass defect of a molecule without empirical mass

    Hello, I'm currently writing a chemistry program. The user can create any kind of atom he can imagine, and then combine them into molecules. To properly calculate all the energies involved I need a formula to calculate the mass defect of a nucleus. I mustn't use empirical data to allow for...
  18. M

    What's the relation between Mass Defect and the Strong Nuclear Force?

    Hello. Sorry for being annoying, I've posted like three questions today. But I'm studying nuclear chemistry and still somewhat confused regarding the binding energy and mass defect and their relation with the strong nuclear force.. 1) in this Hank Green video... He says that the mass defect...
  19. M

    Mass defect and binding energy help

    I don't know if I completely understand mass defect and binding energy so I will write what I understand and hopefully you can explain any misunderstandings I have. I know what mass defect is and that I understand that we need the strong nuclear force to keep the nucleus together etc. but I...
  20. N

    Energy-mass equiliance and mass defect

    Hi! According to E=mc^2, we have the phenomena mass defect. For example, when we put a proton and neutron together, that particle has a slightly lower mass than the sum of mass of the free particles due to the binding energy between the nucleons. OK, I'm fine with that - a lower energy results...
  21. J

    Nucleons, mass defect, and mass

    in high school we are learning about mass defect in nuclear fission and fusion and I know the math: ΔE=Δmc^2 however often the mass changed into energy is much less then the mass of a single nucleon(proton or neutron) and there are no fewer nucleons. for this to happen I would think that you...
  22. 4

    Mass Defect to calculate the stability of a nucleus

    This is just a simple conceptual question. When we try to calculate a nuclear binding energy of some nucleus, we get the mass defect(del M) and find the binding energy by using (del M)c^2 right? Well, what I do not understand is this. For instance, let's take a formation of a...
  23. M

    Mass defect - where does it go to?

    In nuclear physics, when two nucleons (e.g. a proton and neutron) fuse together, they release binding energy. There is a mass discrepancy between the newly formed deuterium nucleus and the initial mass of both nucleons. This mass defect is related to the binding energy by the famous...
  24. J

    Understanding the Mass Defect in Nuclei

    Why is there a mass defect in the nucleus? I think about mass defect in this way - A comparatively unstable nucleus( i.e. low binding energy) converts to a stabel nucleus( high binding energy) Intially internal energy was U1 and then it became U2. So when it converts then some energy...
  25. A

    Simple Mass Defect Calculation

    Homework Statement Find the mass defect of O-15. 2. The attempt at a solution I've see a couple different suggested ways for computing the mass defect and I want to know if I'm doing this correctly. Mass of O-15 = 13,975 MeV/c^2 Proton mass = 938.3 MeV/c^2 Neutron mass = 939.6...
  26. S

    Mass Defect & the Strong Force in Nucleons

    I was wondering how mesons or the strong force is accounted for in mass defect. Nucleons individually have more mass then when they are bound together in a nucleus of an atom. I saw a teacher/professor speak on youtube. He said the binding energy (strong force) was calculated as part of the...
  27. I

    Calculating the Mass Defect of 40Ca

    Homework Statement What is the mass defect of the 40Ca nucleus? Homework Equations Δm=(Zmp+(A-Z)mn)-m The Attempt at a Solution mass of 40Ca=40.078 amu mass of proton in amu is mp=1.0073 amu mass of neutron is mn=1.0087 amu atmomic number of 40Ca is Z=20 its mass number is...
  28. D

    Mass Defect of 7Li Nuclues

    Homework Statement What is the mass defect of the 7Li nucleus (A = 7)? Homework Equations mass of 7Li nucleus per atomic table is 7.016004 u N = A-Z or #neutrons = 7-3 = 4 computed mass of proton and neutrons in nucleus = 3 p*mass of p + 4n *mass of n mass of proton = 1.00726 u mass of...
  29. A

    Gravitational mass defect, weyl metric

    hello everyone, following the book of Landau&Lifsitz I managed to understand the Schwarzschild solution. At the end, it finds this formula for the mass of the spherical body generating the gravitational field: M=\frac{4\pi}{c^2} \int^a_0 \epsilon(r) r^2 dr in which \epsilon(r) is...
  30. R

    Mass Defect of Hydrogen-2 Electron Binding Energy

    Homework Statement : the binding energy for the electron in the ground state of hydrogen-2 is 13.6ev what is the corresponding mass defect of the hydrogen atom in amu (atomic mass units) not sure if you need atmoic mass of the hysgrogen atom its given to be 2.014102u Relevant equations: not...
  31. J

    Quick question about positive beta decay and mass defect?

    Hi, I was wondering about something in my notes that I don't quite understand. In positive beta decay in nuclear physics, we have a proton becoming a neutron and kicking out a positron and an electron neutrino (which is assumed massless here). In the expression for the energy released, Q =...
  32. JK423

    Why is there a mass defect in the nucleous?

    Can someone explain to me why is there a mass defect in the nucleous? That is, why the nucleous' mass is smaller than the sum of the masses of its constituents (nucleons)? PS. Just to inform you about my background, I am in the 4rth year in physics. The funny thing is that i was first taught...
  33. M

    Mass Defect: Proton and Neutron Weight Change?

    I understand that when two nuclei combine to form another nuclei . the resultant nucleon will have a lower mass than the some of the two parent nuclei. I also understand that the missing mass has been given out as energy... Does this mean that the protons and neutrons have actually gotten...
  34. P

    Mass defect of a nucleus

    What is the mass defect of the 15N nucleus? My attempt: 15-7=8 7(1.008665)+8(1.0078225)-14.003074 =1.120161 the answer needs to be in u so i don't know if this makes a difference or not but for some reason it is not working
  35. J

    Calculate Mass Defect of Nitrogen

    Homework Statement For the common isotope of nitrogen, 14N, calculate the mass defect. Homework Equations \DeltaM = Zmp + Nmn - M The Attempt at a Solution 7(1.00727646688)+7(1.00866491560)-14.003074 \DeltaM = .108516177 Masteringphysics says this is wrong. says i may...
  36. K

    Nuclear Physics - Mass Defect & Binding Energy

    [SOLVED] Nuclear Physics - Mass Defect & Binding Energy 1. Carbon 12 (^{12}_{6}C) has a nuclear mass of 1.99264 x 10-26 kg, a proton has a mass of 1.67353 x 10-27, and a neutron has a mass of 1.67492 x 10-27 kg. Calculate the mass defect for carbon 12. My equation looks like this...
  37. S

    Nuclear Chemistry: Explaining Binding Energy and Mass Defect

    I'm doing a nuclear chemistry project right now, and I am able to solve all of the problems involving binding energy and mass defect, however I have one conceptual question. Why is it that when the nucleons combine with each other they let off energy? At first I thought it was their kinetic...
  38. S

    B.) Mass Defect & Binding Energy for Astatine 21885At

    1. For astatine 21885At (atomic mass = 218.008684 u) obtain each of the following: (a) The mass defect in atomic mass units wrong check mark u (b) the binding energy (in MeV) MeV (c) the binding energy per nucleon (in MeV) MeV 2. Shown in atempt...
  39. M

    Mass Defect: Pb-210 Nuclear Binding Energy

    Homework Statement For lead N=210 Z=82 Pb (atomic mass = 209.984163 u) obtain each of the following: (a) The mass defect in atomic mass units u (b) the binding energy (in MeV) MeV (c) the binding energy per nucleon (in MeV) MeV Homework Equations The Attempt at a...
  40. K

    Do galaxies have a negative mass defect?

    http://en.wikipedia.org/wiki/Binding_energy#Mass_Defect But the opposite is true for galaxies! Quarks too! Their mass appears to be larger than their constituents as well...
  41. denian

    Why there is mass defect?

    why there is mass defect in a nuclide? thank you.
  42. benzun_1999

    Mass Defect Explained

    Dear reader, My friend was telling about something called mass defect. what is it correctly? -benzun All For God