Nuclear Chemistry

## Hadrons (Optional)

Hadron is a composite particle made up of quarks and mesons held together by strong force .

## Subatomic Particles (Optional)

1) Positron (anti-electron) : The positron has charge + 1 and same mass as electron (negligible) .

Notations : β+ e+ . When electrons and positrons collide , they give rise to 2 or more gamma photon rays .

2) Lepton : Particles that are subject to Pauli's Exclusion Principle . consists of (e- ve)(μ- vμ)(t vt)

3) Neutrinos : It is electrically neutral , with half integer spin . Neutrinos are leptons along with charged electrons , muons(μ) , taus ; and come in three flavors : electron neutrinos(ve)(-1/2 spin) , muon neutrinos(vμ) (+1/2 spin), tau netutrinos (vt) (+1/2) .

For every electron neutrino produced , a positron is produced and for every electron anti-neutrino produced , an electron is produced as well .

4) Anti-Neutrino : Anti-Neutrino helps in conservation of Lepton Number .

5) Quark : Quarks combine to form hadronic particles , of which protons and neutrons are the most stable . types or flavors : up , down , strange , charm , top , bottom .

6) Anti-Quark : Some properties of anti-quark have equal magnitude and opposite sign of that of quarks .

7) Mesons : A Meson is composed of a quark and anti-quark , bound together by strong interactions .Mesons are very unstable . The longest life of a meson could be a hundredth of a microsecond . Charged mesons decay to give electrons and Neutrinos . Uncharged Mesons may decay to give photons .

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## Nuclear Coulombic Barrier

The force of repulsion between the nucleus and approaching α particle is called as Nuclear Coulombic Barrier .

Repulsive Potential Energy = V = (Z1e)(Z2e) / d = (Z1Z2)e2 / d

## The Nucleus

**Nuclear Size**

r = r0A1/3 {where r = nuclear size , A = Atomic mass number}

r0 = 1.4 x 10-15 m = 1.4 fm

**Nucleus Proton Ratio**

Nuclei with even number of protons and neutrons are abundantly found .

Nuclei with even - odd combination are intermediately found .

Nuclei with odd - odd combination are rare .

**Nuclear Stability**

The Nucleus Proton Ratio gives us an idea of the stability of a nucleus .

As atomic Number increases , the N/P ratio increases . (This is because the more number of neutrons are added than protons .)

All nuclei above atomic number 82 , are beyond stability belt and are radioactive .

## Radioactive Decay

Radioactive Decay takes place in order to stabilize the nucleus . In the process the atom may gain or loss it's entities .

**α Emission**

It is equivalent to a Helium Atom . An α emission eliminates 4 amu and 2 Z from an atom .

Almost all elements above atomic number 82 decay by α emission . It leads to the formation of isodiapher i.e. difference in number of Neutrons and Protons remains same .

**β Emission**

It is equivalent to conversion of a neutron to proton . Thus , A β emission adds 1 Z to an Atom . A neutron is converted into a proton by removal of negative charge from it .

Elements having a very high N/P ratio and that lie above the stability belt , undergo β emission , as neutrons are converted into protons are added .

**Positron Emission**

It is equivalent to a particle having no mass but positive charge . This particle is called as a positron .

It is actually the conversion of proton to neutron by removing it's positive charge .

A positron emission or β+ emission eliminates 1 Z from the atom .

**Electron Capture (K Capture)**

It is equivalent to an electron from K shell . In this emission , an electron from K shell is captured by the nucleus . AS an effect , a proton is converted into a positron . Electron capture mostly occurs with Heavier elements .

**γ Emission**

It is equivalent to a neutron . γ Emission causes no change .

## Nuclear DisIntegration

**Rate of DIsintegration**

Rate of DIsintegration = - dN/dt

Rate α N

Rate = λ N

**Integrated Rate Law**

λ = [2.303/t] log10 [N0/N]

N0/N gives the ratio of number of atoms , or the ratio of number of moles .

**Simultaneous Decay**

Decay pf an equimolar binary mixture .

2.303 log10[N1/N2] = (λ2 - λ1) t

**Half Life Period**

t1/2= 0.693 / λ Also ; at any point ; N = 2-n N0

**Average Life Period**

λ' = 1/λ = t1/2 / 0.693 = 1.44 t1/2

## Radioactivity

**Unit**

The standard unit of radioactivity is Curie . The biological effect of radiation is measured in rads .

**Parallel Radioactive Disintegration**

Suppose a Nuclei A splits into nuclei X and Y , then

λA = λX + λY

Fractional Yield of X = λX / λA

Fractional Yield of Y = λY / λA

**Successive Radioactive Disintegration**

Daughter Nuclei , formed by parent nuclei also undergoes disintegration .

Suppose A forms B and B forms C with λ1 and λ2 as disintegration constants ;

N1/N2 = (λ2 - λ1) / λ1

**Secular Equilibrium**

N1 / N2  = λ2 / λ1

i.e. radioactivity is not affected through the half-lives

**Disequilibrium**

## Fission and Fusion Reactions

**Nuclear Fusion**

Nuclear fusion is the process in which lighter nucleus combines to form a heavier nucleus , which results in the emission of enormous amount of energy .

e.g. A Hydrogen bomb releases 17.6 MeV energy .