physics-class-12-unit-12-chapter-09-the-structure-of-the-atom-l-9-9-flzxgo3pbnw

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>De Broglie waves</B></Primary></p>
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<p><strong>Structure of the Atom</strong></p>
<p>$ 2d \sin \theta = n \lambda $</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-5.jpg"></p>
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<footer style='font-size:18px'><span style="color:blue">De Broglie waves</span>$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Light</B></Primary></p>
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<p>$ E = h v ; v = c = v\lambda$</p>
<p>$ v = \frac {c}{\lambda}$</p>
<p>Planck : $ E = \frac {hc}{\lambda}$</p>
<p>Maxwell $ \bigcup_v = \pi c$</p>
<p>$\left[\therefore \bigcup = \text{Energy density}, \pi = \text{Mom density}\right]$</p>
<p>n $\rightarrow$ Number density of photons.</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-6.jpg"></p>
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<footer style='font-size:18px'>De Broglie waves$\rightarrow$<span style="color:blue">Light</span>$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Photon Energy</B></Primary></p>
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<p>Each photon carries an energy hv.</p>
<p>c = $v\pi$</p>
<p>$\therefore \bigcup_v= nhv = \pi_v c$</p>
<p>$\pi_= \frac {nhv}{c} = \frac {nh}{\pi}$</p>
<p>$\frac {h}{\pi}$ is the momentum carried by each photon.</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-7.jpg"></p>
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<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$<span style="color:blue">Photon Energy</span>$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Matter</B></Primary></p>
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<p>$V_{wave} = v\lambda = \frac {E}{p}$</p>
<p>$V^{WR}_{part} = \frac {p}{m}$</p>
<p>$V^{re}_{part} = \frac{pc^2}{\epsilon}$</p>
<p>There is a Discrepancy.</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-9.jpg"></p>
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<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$<span style="color:blue">Matter</span>$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Particle Speed</B></Primary></p>
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<p>$V=v\lambda$</p>
<ul>
<li>It appears as if the wave associated with the electron, & the particle move with different speeds.</li>
</ul>
<p>$V_w = \frac{V_p}{2}$ for NR case.</p>
<p>$ = \frac{c^2}{v} $ for relativistic case.</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-10.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$<span style="color:blue">Particle Speed</span>$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Structure of the Atom</B></Primary></p>
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<p><strong>Pilot waves</strong></p>
<p><strong>Structure of the Atom</strong></p>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/aaf9e5fe-3338-4b65-35ea-1699de717600/public" width="80%" >


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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$<span style="color:blue">Structure of the Atom</span>$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Early Speculations</B></Primary></p>
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<p><strong>India :</strong> Kanda (Vaisheshika School)</p>
<p><strong>Greece:</strong> Democritus</p>
<p><strong>England:</strong> Isaac Newton , Dalton…………</p>
<p><strong>Other schools :</strong> The great elements (Greece, India)</p>
<p><strong>Structure  of the Atom</strong></p>
<ul>
<li>Indian Atomic School</li>
<li>Atom:</li>
<li>Molecule : Two atoms:</li>
</ul>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-12.jpg">
<img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-12a.jpg"></p>
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<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$<span style="color:blue">Early Speculations</span>$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Indirect Evidence</B></Primary></p>
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<ul>
<li>Priestly</li>
<li>Lavoiser</li>
<li>Dalton</li>
<li>Mendeleeve</li>
<li>Mary and Pierre Curie, Becquerel</li>
<li>Atom are fundamental units of chemical reaction</li>
<li>Consequence: May or may not be the ultimate constituents of matter</li>
</ul>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-13.jpg">
<img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-13a.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$<span style="color:blue">Indirect Evidence</span>$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Models of Atoms</B></Primary></p>
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<p><strong>Two major Contenders</strong></p>
<ul>
<li>Plum pudding model (Thompson)</li>
<li>Planetary Model (Rutherfor)</li>
</ul>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/a4a410d4-3e2c-4e47-ac84-c274ec93e500/public" width="80%" >
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/264e8e2f-31de-4786-637d-4e9e6b31a200/public" width="70%" >


</div>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$<span style="color:blue">Models of Atoms</span>$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Models of Atoms</B></Primary></p>
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<p><strong>Source :</strong> ${ }^{214}_{83} Bi;$</p>
<p>Energy of $\alpha$ particle 5.5 MeV</p>
<p><strong>Target:</strong> A very thing gold foil $(2.1 \times 10{-7})$</p>
<p><strong>Detector :</strong> Zinc Sulphide (scintillation) + Microscope.</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-15.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$<span style="color:blue">Models of Atoms</span>$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Models of Atoms</B></Primary></p>
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<div style='float: left; width:0%;font-size:22px;text-align:left;'>
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 <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/264e8e2f-31de-4786-637d-4e9e6b31a200/public"  width="40%" > 
</div>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$<span style="color:blue">Models of Atoms</span>$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Rutherford Cross-Section</B></Primary></p>
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<div style='float: left; width:0%;font-size:22px;text-align:left;'>
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<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/297a31f8-d675-47c9-e4e6-ca57e1977500/public"  width="40%" > 

</div>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$<span style="color:blue">Rutherford Cross-Section</span>$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Modelling the Results</B></Primary></p>
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<p><strong>Important features</strong></p>
<ul>
<li>Most of the electrons are unscattered. They just pass through undeflected.</li>
<li>The number of electrons getting back scattered is relatively quite large.</li>
</ul>
<p><strong>Basic assumption</strong></p>
<ul>
<li>Atom has a size of in the range of angstroms</li>
</ul>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-18.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$<span style="color:blue">Modelling the Results</span>$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Analysis of the Rutherford Experiment</B></Primary></p>
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<center>
<img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/bcf21179-d213-4305-722c-7135ab83e400/public" width="48%" >
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-19.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$<span style="color:blue">Analysis of the Rutherford Experiment</span>$\rightarrow$Atom</footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Analysis of the Rutherford Experiment</B></Primary></p>
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<p>$m_c = 0.5 Mev /c^2$</p>
<p>$m_{\alpha} = 4 GeV/c^2$</p>
<p>1MeV = $10^6$ eV</p>
<p>$\frac {m_e}{m_\alpha} = \frac {0.5 \times 10^6}{4 \times 10^9} \approx 10^{-4} $</p>
<p>8000 = $\frac{1}{8000}$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-20.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$<span style="color:blue">Analysis of the Rutherford Experiment</span>$\rightarrow$Atom</footer>
<p>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Atom</B></Primary></p>
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<div style='float: left; width:99%;font-size:22px;text-align:left;'>
<ul>
<li>All scattering is essentially due to the positive charges.</li>
<li>Detector is important.</li>
<li>R cannot be greater than the size of the Atom.</li>
</ul>
<p><strong>Atom Size</strong></p>
<p>$R \leq 10{-10}m$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-21.jpg">
<img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-21a.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$<span style="color:blue">Atom</span></footer>

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Structure of the Atom</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Atom</B></Primary></p>
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<p>$\gamma_{min} = \frac {87 \times 2 \times e^2}{4 \pi \epsilon_0 \times 5.5 MeV}$</p>
<p>$ \approx 10{-14}m$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-09-The-Structure-of-The-Atom-L-9-9-flzxgo3pbnw-22.jpg"></p>
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<hr>
<footer style='font-size:18px'>De Broglie waves$\rightarrow$Light$\rightarrow$Photon Energy$\rightarrow$Matter$\rightarrow$Particle Speed$\rightarrow$Structure of the Atom$\rightarrow$Early Speculations$\rightarrow$Indirect Evidence$\rightarrow$Models of Atoms$\rightarrow$Rutherford Cross-Section$\rightarrow$Modelling the Results$\rightarrow$Analysis of the Rutherford Experiment$\rightarrow$<span style="color:blue">Atom</span></footer>