physics-class-12-unit-13-chapter-02-the-atomic-nucleus-masses-and-stability-i-l-2-5-bij7ibo9gsg

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Nuclear Saturation </primary>
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- $\rho_{\text {ch }}=$ constant in the nuclear volume

- $e^{-}$scathering

- $\rho$ matter = constant

- M(A) = $M_0$ A

- microscapic defferences

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<footer style = "font-size: 18px">The Atomic Nucleus Masses and Stability $\rightarrow$ Nuclear Saturation $\rightarrow$ <span style = "color:blue"> Nuclear Saturation </span> $\rightarrow$ More on Nuclear Masses $\rightarrow$ Mass Energy Equivalence </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> More on Nuclear Masses </primary>
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- **Mass Energy Relation 1**

- No material particle can move with a speed $v \geq c$
- There is no restriction on the energy a body can possess
- Therefore, $p \neq m v, E \neq \frac{1}{2} m v^2$
- Inertia depends on the speed!

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<footer style = "font-size: 18px">Nuclear Saturation $\rightarrow$ Nuclear Saturation $\rightarrow$ <span style = "color:blue"> More on Nuclear Masses </span> $\rightarrow$ Mass Energy Equivalence $\rightarrow$ Mass Defect and Binding Energy </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Mass Energy Equivalence </primary>
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- **Einstein Relation**

- $M(v)=M_0 \frac{1}{\sqrt{\left(1-v^2 / c^2\right)}}$

- $E=M(v) c^2$

- $p(v) = M(v)v$

- $E^2 = p^2 c^2 + M_0^2 c^4$

- **Mass Speed Relation**

- $\beta = v/c$

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<footer style = "font-size: 18px">Nuclear Saturation $\rightarrow$ More on Nuclear Masses $\rightarrow$ <span style = "color:blue"> Mass Energy Equivalence </span> $\rightarrow$ Mass Defect and Binding Energy $\rightarrow$ Binding Energies </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Mass Defect and Binding Energy </primary>
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- **Stability issues**

- $ E = Mc^2$

- $ \Delta E = (\Delta M)c^2$

- Units and Dimensions
- Atomic Mass Units: ${ }_6^{12} C \equiv C$

- $1 u \equiv \frac{M_C}{12}=1.660539 \times 10^{-15} \mathrm{~kg}$

- $M_p$ & =1.00727 u

- $M_n$ & =1.008664 u

- $M_{c l}^{35(37)}$ & =34.98(36.98) u

- Masses : SI unit kg inconvenient

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<footer style = "font-size: 18px">More on Nuclear Masses $\rightarrow$ Mass Energy Equivalence $\rightarrow$ <span style = "color:blue"> Mass Defect and Binding Energy </span> $\rightarrow$ Binding Energies $\rightarrow$ Binding Energies </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Binding Energies </primary>
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- **Mass Defect**

- $\Delta M_X$={$Z M_p+(A-Z) M_N$}-$M_X$

- $(BE)_X = \Delta M_X \times c^2$

- Masses : SI unit kg inconvenient

- $M_H$ : $M_P$ : $M_e$

- $e^{-}$to $\infty$

- 13.6ev

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<footer style = "font-size: 18px">Mass Energy Equivalence $\rightarrow$ Mass Defect and Binding Energy $\rightarrow$ <span style = "color:blue"> Binding Energies </span> $\rightarrow$ Binding Energies $\rightarrow$ Binding Energies </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Binding Energies </primary>
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- **Mass Defect**

- $\Delta M_X = \\{Z M_p+(A-Z) M_N \\} - M_X$

- $(BE)_X = \Delta M_X \times c^2$

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<footer style = "font-size: 18px">Binding Energies $\rightarrow$ Binding Energies $\rightarrow$ <span style = "color:blue"> Binding Energies </span> $\rightarrow$ Hydrogen Atom $\rightarrow$ Hydrogen Atom </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Hydrogen Atom </primary>
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- $e^- \rightarrow \infty$

- 13.6ev

- He

- $(BE)_{1^{st} electron}$

- $= (BE)_{Bohr}$

- repulsion

- $e^- - e^-$ repulsion

- not ionised

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<footer style = "font-size: 18px">Binding Energies $\rightarrow$ Binding Energies $\rightarrow$ <span style = "color:blue"> Hydrogen Atom </span> $\rightarrow$ Hydrogen Atom $\rightarrow$ More on Binding Energy per Nucleon </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> More on Binding Energy per Nucleon </primary>
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- **Saturation Property**

- Fe (56) has the largest binding energy per nucleon: $8.75 \mathrm{MeV}$

- Roughly constant in the range $30 \leq A \leq 170 \mathrm{MeV}$

- Has smaller values for both $A$ small, and $A>200$

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<footer style = "font-size: 18px">Hydrogen Atom $\rightarrow$ Hydrogen Atom $\rightarrow$ <span style = "color:blue"> More on Binding Energy per Nucleon </span> $\rightarrow$ Implications $\rightarrow$ Interesting Aspets of Nuclear Forces </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Implications </primary>
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- **Food for thought**

- Neutrons are as strongly bound as protons in the Nucleus

- Protons are bound to each other with same strength

- Nuclear forces much stronger than the Coulomb repulsion

- Saturation suggests that Nuclear forces are short ranged

- Energetics for understanding radioactivity, fusion and fission

- **Protons** : Positicaly electrically charged

- **Neutrons** : Not charged electrically

- Magnetic moment

-1.91

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<footer style = "font-size: 18px">Hydrogen Atom $\rightarrow$ More on Binding Energy per Nucleon $\rightarrow$ <span style = "color:blue"> Implications </span> $\rightarrow$ Interesting Aspets of Nuclear Forces $\rightarrow$ Interesting Aspets of Nuclear Forces </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Interesting Aspets of Nuclear Forces </primary>
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- **1.** Nuclear forces are strong.

- **2.** Are they always attractive?

- **Ans - No**

- $^1 _1 H$ $\rightarrow ^1p$

- $^2 _1 H$ <ins>deuteron</ins> $^1p ; 1n$

- $^3 _1 H$ <ins>Trititum</ins> $^1p ; 2n$

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<footer style = "font-size: 18px">More on Binding Energy per Nucleon $\rightarrow$ Implications $\rightarrow$ <span style = "color:blue"> Interesting Aspets of Nuclear Forces </span> $\rightarrow$ Interesting Aspets of Nuclear Forces $\rightarrow$ Interesting Aspets of Nuclear Forces </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Interesting Aspets of Nuclear Forces </primary>
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- $^3 _2 He$ : 2 protons, 1 neutron

- $^4 _2 He$ : 2 Protons, 2 neutrons

- $^{12} _6 He$ : 6 Protons, 6 neutrons

- $^{16} _8 O$ : 8 Protons, 8 neutrons

- $^{235} _{92} U$ : 92 Protons, 235-92 = 143 neutrons

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<footer style = "font-size: 18px">Implications $\rightarrow$ Interesting Aspets of Nuclear Forces $\rightarrow$ <span style = "color:blue"> Interesting Aspets of Nuclear Forces </span> $\rightarrow$ Interesting Aspets of Nuclear Forces $\rightarrow$ Most Dramatic </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Most Dramatic </primary>
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- No Nuclear with only protons

- No Nuclear with only neutrons

- **1.** Nuclear force between two protons is repulsive.

- **2.** Nuclear force between two neutrons is also repulsive.

- **3.** force between a proton and a neutron can be attractive.

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<footer style = "font-size: 18px">Interesting Aspets of Nuclear Forces $\rightarrow$ Interesting Aspets of Nuclear Forces $\rightarrow$ <span style = "color:blue"> Most Dramatic </span> $\rightarrow$ Implications $\rightarrow$ Some Questions </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Implications </primary>
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- **Food for thought**

- Neutrons are as strongly bound as protons in the Nucleus    
- Protons are bound to each other with same strength
- Nuclear forces much stronger than the Coulomb repulsion
- Saturation suggests that Nuclear forces are short ranged
- Energetics for understanding radioactivity, fusion and fission

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<footer style = "font-size: 18px">Interesting Aspets of Nuclear Forces $\rightarrow$ Most Dramatic $\rightarrow$ <span style = "color:blue"> Implications </span> $\rightarrow$ Some Questions $\rightarrow$ Nuclear Forces </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Nuclear Forces </primary>
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- **Million dollar question**

- Electrical Charge independence
- Nuclear Charge dependence
- Strong interaction
- Short range

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<footer style = "font-size: 18px">Implications $\rightarrow$ Some Questions $\rightarrow$ <span style = "color:blue"> Nuclear Forces </span> $\rightarrow$ Some Illustrative Data $\rightarrow$ Proton Gas </footer>

### <Success style="font-size:25px"> The Atomic Nucleus Masses And Stability I L-2 </Success>
### <primary style="font-size:24px"> Proton Gas </primary>
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- $\frac{3}{2} k T=\frac{1}{4 \pi \varepsilon_0} \frac{e^2}{R}$

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<footer style = "font-size: 18px">Nuclear Forces $\rightarrow$ Some Illustrative Data $\rightarrow$ <span style = "color:blue"> Proton Gas </span> $\rightarrow$ Fusion in Sun $\rightarrow$ Thank You </footer>