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Gadget of Mass

Atomic mass product (amu) and electron volt (eV)

Inside of the exploration of atomic and nuclear physics hundreds are expressed within just atomic mass system abbreviated amu and energies are expressed inside electron volt abbreviated eV.

The atomic mass gadget is explained as a single-twelveth of the mass of the carbon atom gC12. It is expressed inside kg (SI product of mass) as follows :

The amount of atoms of gC12 inside 1 mole of carbon is 6.0221367 x 1023 (Avagadro amount). This indicates that mass of 6.0 2 2 1 36 7 x 1023 atoms of 6C12 = 12 g = 12 x 10-3 kg.

r i ♦ f ^12 12 x 10~3 Mass of 1 atom of 6C =-kg

6.0221367 x10

1 12 1 amu = — x mass of 1 atom of 6C

12

-3

= —x— 12 x 10-— = 1.6605402 x 10~27 kg

12 6.0221367 x 10

Hence, 1 amu (or conveniently 1 u) is virtually 1.661 x 10~27 kg.

The electron volt is explained as the electrical energy realized by means of an electron Whilst it is accelerated in the course of a foreseeable future big difference of 1 volt. It is expressed within joule (SI device of electricity) as follows :

1 electron-volt = 1 eV = (electron expense) (l volt of p. d.)

= ^1.60217738 x 10~19 coulomb j (l volt)

= 1.60217738 x lO-19 joule Therefore, just one electron-volt is approximately equivalent in direction of 1.602 x 10~19 J

Relation among amu and eV (1 amu = 931 MeV)

Atomic mass machine is a gadget of mass despite the fact that electron volt is a machine of electricity. The equivalence concerning them can be accomplished versus Einstein’s mass-electric power relation. In accordance in direction of Einstein, the electricity identical of a sure mass ‘m’ is E = mc2 where by

97

c is the pace of light-weight within just cost-free spot. At the moment, 1 amu of mass is 1.6605402 x 10 kg. That’s why its electrical energy very similar is supplied by way of

2

£ = m (inside kg) c2 (ms-1)

2

= 1.6605402 xlO-27 (kg) ^2.99792458 xl08j m2s~2

– 1.6605402 x 8.98755179 x 10~27 x 1016 kg m2s~2 E = 1.6605402 x 8.98755179 x 10″” J

. ‘ 1.6605402 x 8.98755179 xlO”11 ‘ r , „ t’nnt„no 1n-19 ,1 i.e., E =–— eV v 1 eV = 1.60217738 x10 J

1.60217738 x 10 L J

= 9.314 xlO8 eV

E = 931.4 x 106 eV

i.e., E ~ 931 MeV v 106 eV = 1 Mevj

Therefore, electric power identical of 1 amu of mass is approximately 931 MeV. Observe :

The atomic mass scale is a clean mass scale followed as a result of worldwide union of natural and employed physics within 1960 toward evaluate atomic and nuclear hundreds. It is stated within words of the mass of 6C12 atom which is the maximum wealthy and solid isotope of carbon. This scale is way too identified as isotopic mass scale. As a end result, mass of an atom or that of the nucleus of an atom is termed its isotopic mass.

Mass defect

Choose the nucleus of an atom of atomic selection Z and mass range .4, lzXA], It includes Z protons and (A – Z) neutrons. If mp and mn are the no cost country chill out loads of a proton and a neutron respectively then the take it easy mass of the nucleus is [Z (m ) + (A – Z) mn). It is discovered that the relax mass M of a nucleus as attained versus scientific tests is generally fewer than the quantity mass of its constituent debris. This is found out in direction of be accurate for all reliable nuclei. The big difference among the mass of the nucleus and the quantity of the totally free nation take it easy loads of its constituent debris is recognised as mass defect, denoted by way of Am. Therefore, mass defect of a nucleus is

Am = [z (mp) +(A-Z) #n„] – M

Binding electricity

It is uncovered that there is a sure mass defect (“dropped” mass) connected with each good nucleus. The theoretical motive for this ‘lost’ mass is centered upon Einstein’s mass-electrical power relation. If A m be the mass defect of the nucleus of an atom of atomic amount Z and mass range A then the electric power produced through the development of the nucleus is = (A m) c2. It is referred to as the binding electric power of the nucleus. This indicates that the amount of money electricity of all the nucleons in just their certain region (the moment in the nucleus) is. much less than the sum electric power of the similar nucleons within just their absolutely free nation. That’s why, binding electrical energy of a nucleus can far too be explained as the over-all electric power toward be provided in the direction of split the nucleus thoroughly into its constituent debris.

Attempt the lightest solid atom made up of additional than a person nucleon particularly, the deuteron. It is made up of 1 proton and a single neutron within just the nucleus. Consequently, the mass of H2 is [mp + mn] = 1.007825 + 1.008665 = 2.01649 u. The experimental mass of ,//2 atom is discovered in direction of be 2.014102 u. This demonstrates that the mass defect of XH2 is Am = 2.016490 – 2.014102 = 0.002238 u. The electricity comparable of this mass is the binding electrical power of jH2

i.e., Eb =(Am)c2 =(0.002238 u) (931.4) MeV/u = 2.224 MeV

This exhibits that electricity essential toward split a deuterium nucleus into a neutron and a proton is 2.224 MeV and scientific studies contain proved this final result.


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