physics-class-12-unit-13-chapter-03-the-atomic-nucleus-masses-and-stability-ll-l-3-5-nvhbdxjznta

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Nuclear Forces</B></Primary></p>
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<p><strong>Million dollar question</strong></p>
<ul>
<li>Electrical Charge independence</li>
<li>Strong interaction</li>
<li>Short range</li>
</ul>
<p><strong>EM Interaction</strong></p>
<p>$\frac{e^2}{r}= V(r)$</p>
<p>$V(r)^{\lambda}=\frac{e^{\mu r}}{r}$</p>
<p>$\mu=\frac{1}{r}$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Nuclear Fusion in Sun</B></Primary></p>
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<p><strong>The deuteron production: Weak process</strong></p>
<p>$^1 \mathrm{H}_1+{ }^1 \mathrm{H}_1 \rightarrow{ }^2 \mathrm{He}_2$</p>
<p>$^2 \mathrm{He}_2 \rightarrow{ }^2 \mathrm{He}_1+\mathrm{e}^{+}+v$</p>
<p>The overall result:</p>
<p>$^1 \mathrm{H}_1+{ }^1 \mathrm{H}_1 \rightarrow{ }^2 \mathrm{He}_1+\mathrm{e}^{+}+v+0.42 \mathrm{MeV}$</p>
<p>Very very slow (Weak Beta Decay!!!)</p>
<p>$e^{+}+e^{-} \rightarrow 2 \gamma+1.02 \mathrm{MeV}$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Nuclear Fusion in Sun</B></Primary></p>
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<p>$2 p+2 n \longrightarrow{ }_2^4 \mathrm{He}$</p>
<p>$4 \mathrm{He} \quad ; \quad 4 \mathrm{He}_2$</p>
<p>$_z^A X \equiv{ }^A X_z$</p>
<p>$V_{\text {coulomb }}=+\frac{e^2}{r}=k T$</p>
<p>Corresponding to $r=10^{-15} \mathrm{~m}$</p>
<p>$T \sim 10^{10} k \quad 10^{10-12} k$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Nuclear Fusion in Sun</B></Primary></p>
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<p><strong>Deuterium</strong></p>
<p>The deuteron production: Weak Process</p>
<p>$^1 \mathrm{H}_1+{ }^1 \mathrm{H}_1 \rightarrow{ }^2 \mathrm{He}_2$</p>
<p>$^2 \mathrm{He}_2 \rightarrow{ }^2 \mathrm{He}_1+\mathrm{e}^{+}+v$</p>
<p>The Overall result:</p>
<p>$^1 \mathrm{H}_1+{ }^1 \mathrm{H}_1 \rightarrow{ }^2 \mathrm{He}_1+\mathrm{e}^{+}+v+0.42 \mathrm{MeV}$</p>
<p>Very very slow (Weak Beta Decay!!!)</p>
<p>$e^{+}+e^{-} \rightarrow 2 \gamma+1.02 \mathrm{MeV}$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Nuclear Fusion in Sun</B></Primary></p>
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<p><strong>The deuteron burning: Strong process</strong></p>
<p>$^2 \mathrm{H}_1 \rightarrow{ }^3 \mathrm{He}_2+\gamma+5.49 \mathrm{MeV}$</p>
<p>How is Helium formed?</p>
<p>$^2 \mathrm{H}_1 \rightarrow{ }^3 \mathrm{He}_2+\gamma+5.49 \mathrm{MeV}$</p>
<p>$(p, n) ;(2 p, n)+\gamma$</p>
<p>$2 \mathrm{H}_1+{ }^1 \mathrm{H}_1 \rightarrow{ }^3 \mathrm{He}_2+\gamma+5.49$</p>
<p>$d+p \rightarrow{ }^3 \mathrm{He}+\text { evergy }$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Helium 3 Burning</B></Primary></p>
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<p><strong>Multiple routes</strong></p>
<p>The First Route</p>
<p>$^3 \mathrm{He}_2+{ }^3 \mathrm{He}_2 \rightarrow{ }^4 \mathrm{He}_2+2{ }^1 \mathrm{H}_1+12.86 \mathrm{MeV}$</p>
<p>$3 \mathrm{He}_2+{ }^3 \mathrm{He}_2 \rightarrow 4 \mathrm{He} + 2 p + 12.86 \mathrm{me}$</p>
<p>$(2 p, i n)+(2 p, i n) \text {. }$</p>
<p>$\rightarrow \underbrace{(2 p, 2 n)}_{4 \mathrm{He}}+2 p$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Helium 3 Burning</B></Primary></p>
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<p>$_4^1 \mathrm{H}+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+6 \gamma+26.7 \mathrm{MeV}$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Other Pathways</B></Primary></p>
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<p><strong>The lithium path</strong></p>
<p>The second route</p>
<p>$^3 \mathrm{He}_2+{ }^4 \mathrm{He}_2  \rightarrow{ }^7 \mathrm{Be}_4+\gamma$</p>
<p>$^7 \mathrm{Be}_4+\mathrm{e}  \rightarrow{ }^7 \mathrm{Li}_3+v+8.5$</p>
<p>$^7 \mathrm{Li}_3+{ }^1 \mathrm{H}_1  \rightarrow 2{ }^4 \mathrm{He}_2$</p>
<p>Similarly two more routes</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Carbon Cycle</B></Primary></p>
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<ul>
<li>Radius of core: $19 %$</li>
<li>Fusion power: 300W/ $/ \mathrm{m}^3$</li>
<li>Protons burnt: $3.6 \times 10^{38} / \mathrm{s} \sim 3 \times 10^9 \mathrm{~kg}$</li>
<li>Power produced: $3.8 \times 10^{26} \mathrm{~J} / \mathrm{s} \sim 10^{27} \mathrm{Wh}$</li>
<li>Percentage of power produced: $91 %$</li>
</ul>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Total Power Genration in the World</B></Primary></p>
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<p>Total power genrated on the earth by humans</p>
<p>$\text { Coal } \longrightarrow 40$ %</p>
<p>$\text { Gas } \longrightarrow 23$ %</p>
<p>$\text { Hydro, Solar, Wind, Oil, Nucler} \longrightarrow 10$%</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
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<p><strong>Total power is</strong></p>
<p>$\frac{25000 \mathrm{TWH}}{24,345}$</p>
<p>$2.5 \times 10^4 \times 10^{12}$</p>
<p>$\simeq 10^{16} \mathrm{WH}$</p>
<p>$\text { Earth } \sim 10^{16}$</p>
<p>$\text { Sun } \sim 10^{27}$</p>
<p>$\frac{P_{\text {sun }}}{P_{\text {End }}} \sim 10^{11}$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Binding Energy per Nucleon</B></Primary></p>
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<p>For the synthesis a temp $T_{H e}$ is required.</p>
<p>For $C$ syntriais we real a tap $T_c$</p>
<p>$\underline{6p}$</p>
<p>$6 c_2=\frac{6 \times 5}{2}=15$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Fusion</B></Primary></p>
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<p><strong>Numbers speak</strong></p>
<p>$M_p=1.007276 u ; \quad M_n=1.008664 u ; \quad M_{H e}=4.002602 u$</p>
<p>$\Delta M \equiv M_{H e}-2 \times\left(M_p+M_n\right)=-0.029278 u$</p>
<p>$(\Delta M) c^2=-28300.7 \mathrm{keV} \equiv-28.3 \mathrm{MeV}$</p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Carbon Cycle</B></Primary></p>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Masses and Stability</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Mass Versus Life Time</B></Primary></p>
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<table>
<thead>
<tr>
<th>Mass (solar masses)</th>
<th>Time (years)</th>
</tr>
</thead>
<tbody>
<tr>
<td>60</td>
<td>3 million</td>
</tr>
<tr>
<td>30</td>
<td>11 million</td>
</tr>
<tr>
<td>10</td>
<td>32 million</td>
</tr>
<tr>
<td>3</td>
<td>370 million</td>
</tr>
<tr>
<td>1.5</td>
<td>3 billion</td>
</tr>
<tr>
<td>1</td>
<td>10 billion</td>
</tr>
<tr>
<td>0.1</td>
<td>1000s billions</td>
</tr>
</tbody>
</table>
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