physics-class-12-unit-13-chapter-01-the-atomic-nucleus-fission-and-radioactivity-l-1-5-qc-uhpaeeaa

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Solar Energy; T = $ 1.5 \times 10^7 K $</B></Primary></p>
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<p><strong>Carbon Cycle</strong></p>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/93970245-40e8-4933-9cfe-6e5ef5652000/public"  width="45%" >







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<p><strong>Death of Stars</strong></p>
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<footer style='font-size:18px'><span style="color:blue">Solar Energy; T = $ 1.5 \times 10^7 K $</span>$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</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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<th>Mass (solar masses</th>
<th>Time (years)</th>
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<td>60</td>
<td>3 million</td>
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<td>30</td>
<td>11 million</td>
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<td>10</td>
<td>32 million</td>
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<td>3</td>
<td>370 million</td>
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<td>1.5</td>
<td>3 billion</td>
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<td>1</td>
<td>10 billion</td>
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<td>0.1</td>
<td>1000s billions</td>
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<img src= "https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/4b612e78-56d5-46ae-172a-a5c18a535400/public" width = "70%">


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<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$<span style="color:blue">Mass Versus Life Time</span>$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Nuclear Fission</B></Primary></p>
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<p>$A \longrightarrow X_1+X_2+H e$</p>
<p>$+n_1 \beta+n_2 \gamma$</p>
<p>$r_1 + r_2 = n_1 $</p>
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<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$<span style="color:blue">Nuclear Fission</span>$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>
<p>======</p>
<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Radioactivity</B></Primary></p>
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<p><strong>Spontaneous probabilistic process</strong></p>
<p>Beta decay</p>
<p>$\beta^{-} \equiv e^{-} ; \quad \beta^{+} \equiv e^{+}$</p>
<p>$\alpha$ decay (alpha $\left.\equiv{ }^4 \mathrm{He}\right)$</p>
<p>$\gamma$ decay (De-excitation)</p>
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<hr>
<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$<span style="color:blue">Radioactivity</span>
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Alpha Decay</B></Primary></p>
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<p><strong>Compound Nucleus</strong></p>
<p>$\alpha - \text {Particle } = {}_2^4 He $</p>
<p>$M ( {} _ {94} ^{240} Pu) \rightarrow M ( {} _ {92} ^{236} U) + M ( {} _ {2} ^{4} He)$</p>
<p>$M_{P U} {^{c^2}}>M_U {^{C^2}}+{M}_{H e} c^2 +$</p>
<p>$\tiny\left[M_P-\left(M_{D_1}+M_{\mathrm{He}}\right)\right] c^2=Q$</p>
<p>$Q- \text {Factor}$</p>
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<hr>
<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$<span style="color:blue">Alpha Decay</span>$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Universal Features of Beta Decay</B></Primary></p>
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<p><strong>Beta decay</strong></p>
<p>${}_z^A X$</p>
<p>$z \rightarrow \text{ Protons }$</p>
<p>$A-z \rightarrow \text{ Neutrons }$</p>
<p><strong>There are no  ${\beta^- \text { or } \beta^+}$</strong></p>
<p>$n \longrightarrow p+e^{-}+\bar{\nu}$</p>
<p>$p^* \longrightarrow n+e^{+}+\nu$</p>
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<hr>
<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$<span style="color:blue">Universal Features of Beta Decay</span>$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Examples of Beta Decay</B></Primary></p>
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<p>$n \rightarrow p+\mathrm{e}^{-}+\bar{v} $</p>
<p>$^{14} {C} \rightarrow^{14} {N}+{e}^{-}+\bar{v}$</p>
<p>$^{10} {C} \rightarrow ^{10} {B}+v+{e}^{+}$</p>
<p><strong>Fundamental Process</strong></p>
<p>$p \longrightarrow n+e^++\nu$</p>
<p>${m_p<m_n}$</p>
<p><strong>Hydrogen is stable</strong></p>
<p>$p^* \rightarrow n+e^{+}+\nu$</p>
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<hr>
<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$<span style="color:blue">Examples of Beta Decay</span>$\to$More Examples$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>More Examples</B></Primary></p>
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<p><strong>Chain reaction</strong></p>
<p>${}_{90}^{232}\text{Th} \rightarrow _{88}^{228}\text{Ra} + _2^4 \text{He}$</p>
<p>${ }_{88}^{228}\mathrm{Ra} \rightarrow _{89}^{228} \mathrm{Ac}+\mathrm{e}^{-}$</p>
<p>${ }_{89}^{228} \mathrm{Ac} \rightarrow _{90}^{228}\mathrm{Th}+\mathrm{e}^{-}$</p>
<p>${ }_{90}^{228} \mathrm{Th} \rightarrow _{88}^{224} \mathrm{Ra}+_2^4 \mathrm{He}$</p>
<p><strong>${\text{Uranium Chain}}$</strong></p>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/999d86a1-f942-40a3-8c13-6ec6de8d4f00/public"  width="100%" >


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<hr>
<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$<span style="color:blue">More Examples</span>$\to$Uranium Chain$\to$Law of Exponential Decay$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Law of Exponential Decay</B></Primary></p>
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<p>$\lambda = \text{SI} (s^{-1}): \text{ Becquerel }$</p>
<p>$\lambda = \text{Ci}\rightarrow \text{ Curie }$</p>
<p>Decay Rate depends on the Population at that Instant</p>
<p>$-R \equiv \frac{\mathrm{dN}(\mathrm{t})}{\mathrm{dt}} =-\lambda N(t) ; \quad \lambda>0$</p>
<p>$R$ is also called activity.
Units of $R$ : Becquerel (SI);
Curie $(\mathrm{Ci})=3.7 \times 10^{10}$ Becquerel</p>
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<hr>
<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$<span style="color:blue">Law of Exponential Decay</span>$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>The Atomic Nucleus Fission and Radioactivity</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Law of Exponential Decay</B></Primary></p>
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<p>Solution of decay equation</p>
<p>$\frac{d N(t)}{d t}  =-\lambda N {(t)}$</p>
<p>$\int_0^t \frac{d N}{N}  =-\lambda \int_0 ^td t^{\prime}$</p>
<p>$\ln \frac{N(t)}{N(0)}  =-\lambda t \quad \quad \Rightarrow N(t) = N_0 e^{-\lambda t}$</p>
<p>$N_0 e^{-\lambda t}=$ <strong>Exponential decay Not a linear decay</strong></p>
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<footer style='font-size:18px'>Solar Energy; T = $ 1.5 \times 10^7 K $$\rightarrow$Mass Versus Life Time$\to$Nuclear Fission$\to$Radioactivity
$\to$Gamma Decay$\to$Alpha Decay$\to$Universal Features of Beta Decay$\to$Examples of Beta Decay$\to$More Examples$\to$Uranium Chain$\to$<span style="color:blue">Law of Exponential Decay</span>$\to$Two Concepts$\to$Half life $(T _{1/2})$$\to$Mean Life$\to$Decay Chain</footer>