Key PointsNuclear binding power is the energy required to split a nucleus of one atom right into its components.Nuclear binding power is provided to recognize whether fission or combination will it is in a favorable process.The massive defect of a nucleus to represent the mass of the power binding the nucleus, and is the difference between the fixed of a nucleus and the amount of the masses of the nucleons that which the is composed.

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TermsnucleonOne that the subatomic particles of the atomic nucleus, i.e. A proton or a neutron.mass defectThe difference between the calculated fixed of the unbound system and also the experimentally measured massive of the nucleus.strong forceThe atom force, a residual pressure responsible for the interactions between nucleons, deriving native the color force.

Binding Energy

Nuclear binding energy is the energy required to break-up a nucleus of an atom into its ingredient parts: protons and neutrons, or, collectively, the nucleons. The binding power of nuclei is always a hopeful number, since all nuclei require net energy to separate them into individual protons and neutrons.

Mass Defect

Nuclear binding energy accounts because that a noticeable difference in between the actual fixed of one atom’s nucleus and also its intended mass based upon the sum of the masses that its non-bound components.

Recall that power (E) and also mass (m) are related by the equation:

E=mc^2

Here, c is the speed of light. In the case of nuclei, the binding power is so good that that accounts because that a significant amount of mass.

The actual fixed is always less than the amount of the separation, personal, instance masses the the ingredient protons and also neutrons due to the fact that energy is removed once when the nucleus is formed. This energy has mass, i m sorry is gotten rid of from the total mass the the initial particles. This mass, known as the fixed defect, is lacking in the resulting nucleus and also represents the energy released when the cell nucleus is formed.

Mass defect (Md) can be calculated together the difference in between observed atomic mass (mo) and that meant from the merged masses that its protons (mp, each proton having actually a mass of 1.00728 amu) and neutrons (mn, 1.00867 amu):

M_d=(m_n+m_p)-m_o

Nuclear Binding Energy

Once mass defect is known, atom binding power can it is in calculated through converting that mass to energy by utilizing E=mc2. Mass have to be in devices of kg.

Once this energy, which is a quantity of joules because that one nucleus, is known, it can be scaled right into per-nucleon and also per-mole quantities. To transform to joules/mole, merely multiply through Avogadro’s number. To transform to joules per nucleon, simply divide through the variety of nucleons.

Nuclear binding power can also apply to situations when the nucleus splits into fragments composed of more than one nucleon; in this cases, the binding energies for the fragments, as compared to the whole, may be either optimistic or negative, depending upon where the parent nucleus and the daughter fragments autumn on the nuclear binding power curve. If new binding energy is easily accessible when irradiate nuclei fuse, or when heavy nuclei split, one of two people of these processes an outcome in the release of the binding energy. This energy—available together nuclear energy—can be offered to develop nuclear power or build nuclear weapons. As soon as a huge nucleus splits right into pieces, excess power is emitted as photons, or gamma rays, and also as kinetic energy, as a variety of different particles space ejected.

Nuclear binding power is additionally used to determine whether fission or blend will it is in a favorable process. For facets lighter than iron-56, combination will release energy since the nuclear binding energy increases with enhancing mass. Elements heavier 보다 iron-56 will generally release power upon fission, as the lighter elements produced contain greater nuclear binding energy. Together such, there is a peak at iron-56 on the atom binding power curve.

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Nuclear binding power curveThis graph shows the atom binding energy (in MeV) every nucleon together a function of the number of nucleons in the nucleus. An alert that iron-56 has the many binding power per nucleon, making it the many stable nucleus.

The rationale for this top in binding energy is the interplay between the coulombic repulsion the the proton in the nucleus, because like fees repel each other, and also the strong nuclear force, or solid force. The solid force is what holds protons and neutrons with each other at brief distances. Together the size of the nucleus increases, the solid nuclear force is only felt between nucleons that room close together, when the coulombic repulsion continues to it is in felt throughout the nucleus; this leads to instability and also hence the radioactivity and fissile nature of the more heavier elements.

Example

Calculate the mean binding power per mole the a U-235 isotope. Present your prize in kJ/mole.

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First, you must calculate the mass defect. U-235 has 92 protons, 143 neutrons, and has an it was observed mass of 235.04393 amu.

M_d=(m_n+m_p)-m_o

Md = (92(1.00728 amu)+143(1.00867 amu)) – 235.04393 amu

Md = 1.86564 amu

Calculate the fixed in kg:

1.86564 amu x frac1 kg6.02214 imes10^26 amu = 3.09797 x 10-27 kg

Now calculation the energy:

E = mc2

E = 3.09797 x 10-27 kg x (2.99792458 x 108fracms)2

E =2.7843 x 10-10 J

Now convert to kJ per mole:

2.7843 imes10^-10fracJoulesatom imes frac 6.02 imes10^23 atomsmole imes frac1 kJ1000 joules = 1.6762 x 1011frackJmole