### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Wave Nature of Matter </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px"> $\rightarrow$ $\rightarrow$ <span style = "color:blue"> Wave Nature of Matter </span> $\rightarrow$ Matter Waves $\rightarrow$ Photoelectric Effect </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Matter Waves </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - **De Broglie Waves** - Historically: Light $\longrightarrow$ Particle $\longrightarrow$ Newton - Light $\longrightarrow$ Wave $\longrightarrow$ Huygens </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px"> $\rightarrow$ Wave Nature of Matter $\rightarrow$ <span style = "color:blue"> Matter Waves </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Question </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Photoelectric Effect </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - **Wave explanation failed** - $E=h \nu^2 \rightarrow$ the energy - carried by each quantum - Energy conservation </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Wave Nature of Matter $\rightarrow$ Matter Waves $\rightarrow$ <span style = "color:blue"> Photoelectric Effect </span> $\rightarrow$ Question $\rightarrow$ Analogy </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Question </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - If a wave can at times behave like a particle, is it possible that the particles can behave like waves? - waves ? - 1905 1913 $\rightarrow$ Standing Waves <!--## Lecture II - 1--> <!--### The de Broglie Revolution Matter Waves--> </div> <div style='float: right; width:0%;'>  <!----> </main> <hr> <footer style = "font-size: 18px">Matter Waves $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Question </span> $\rightarrow$ Analogy $\rightarrow$ Analogy </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Analogy </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - **The Motivation** - The Reasoning - Motivation: Symmetry - Reasoning: By Analogy - **More on analogy** - For light of a given wavelength and frequency, - $E=h \nu=\frac{h c}{\lambda} \equiv p c $ - $p=\frac{h}{\lambda}$ - Extend the relations to Matter also! </div> <div style='float: right; width:0%;'>   </main> <hr> <footer style = "font-size: 18px">Photoelectric Effect $\rightarrow$ Question $\rightarrow$ <span style = "color:blue"> Analogy </span> $\rightarrow$ Analogy $\rightarrow$ Momentum </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Analogy </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $E=h\nu \longrightarrow $ Non-classical - $v=\nu \lambda= C $ - $\lambda=\frac{c}{\nu} $ - $\lambda=\frac{h c}{\nu} $ - $3 \times 10^8 m/s$ - $\nu = \frac{E}{h}$ - $\frac{1}{\nu} = \frac{h}{E}$ </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Question $\rightarrow$ Analogy $\rightarrow$ <span style = "color:blue"> Analogy </span> $\rightarrow$ Momentum $\rightarrow$ Fundamental Relation </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Momentum </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $U = \Pi C$ - $U \rightarrow$ energy density - $\Pi \rightarrow$ Momentum density - $n (h\nu) = n(pC) \rightarrow$ momentum carried by the quantum - $E_\nu = p_\nu C$ - $E = \frac{p^2}{2m}$ </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Analogy $\rightarrow$ Analogy $\rightarrow$ <span style = "color:blue"> Momentum </span> $\rightarrow$ Fundamental Relation $\rightarrow$ De Broglie Conjecture </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Fundamental Relation </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $p = \frac{h}{\lambda}$ - $E_\nu = h\nu \longrightarrow$ Planck + Einstein used as a fundamental Relation </div> <div style='float: right; width:0%;'> <!----> </main> <hr> <footer style = "font-size: 18px">Analogy $\rightarrow$ Momentum $\rightarrow$ <span style = "color:blue"> Fundamental Relation </span> $\rightarrow$ De Broglie Conjecture $\rightarrow$ De Broglie Conjecture </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> De Broglie Conjecture </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $p = \frac{h}{\lambda}$ is a universal relation - It holds for all waves and all matter - $p$ can be $m v$ - $p$ can be $\frac{m v}{\sqrt{h v^2/c^2}} = m v \gamma$ </div> <div style='float: right; width:0%;'> <!----> </main> <hr> <footer style = "font-size: 18px">Momentum $\rightarrow$ Fundamental Relation $\rightarrow$ <span style = "color:blue"> De Broglie Conjecture </span> $\rightarrow$ De Broglie Conjecture $\rightarrow$ Importance of this extension </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> De Broglie Conjecture </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $P_{\text {Newt }}=m_0 v $ - $P_{\text {Einst}}=\frac{m_0 v}{\sqrt{1-v^2 / c^2}}$ - $p=\frac{h}{\lambda}$ is valid even for particles. - $p \longrightarrow$ input - $\lambda \longrightarrow$ output </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Fundamental Relation $\rightarrow$ De Broglie Conjecture $\rightarrow$ <span style = "color:blue"> De Broglie Conjecture </span> $\rightarrow$ Importance of this extension $\rightarrow$ Electron Diffraction </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Importance of this extension </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - **How Important is This Extension? How Non-Trivial?** - Fundamental relations: - $\lambda=\frac{h}{p} $ - $E^2=p^2 c^2+m_0^2 c^4 \text { or } \frac{\mathrm{p}^2}{2 \mathrm{m}}$ </div> <div style='float: right; width:00%;'> <!----> </main> <hr> <footer style = "font-size: 18px">De Broglie Conjecture $\rightarrow$ De Broglie Conjecture $\rightarrow$ <span style = "color:blue"> Importance of this extension </span> $\rightarrow$ Electron Diffraction $\rightarrow$ Electron </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Electron Diffraction </primary> <hr> <main> <div style='float: left; width:50%;font-size:30px;text-align:left;'> - **Experimental Evidence?** - **Bragg Diffraction Condition** - Diffraction from a crystal - $n \lambda=2 d \sin \theta$ </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/4b5d5a7e-86eb-4fd0-45ac-51e2b1044500/public" width="60%" > <!----> </div> </main> <hr> <footer style = "font-size: 18px">De Broglie Conjecture $\rightarrow$ Importance of this extension $\rightarrow$ <span style = "color:blue"> Electron Diffraction </span> $\rightarrow$ Electron $\rightarrow$ Wave </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Electron </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - **Tennisball** - $\lambda = \frac{h}{p}$ - $10^{-30} 10^{-34}cm$ - Very very hight particles - Electron: $0.5 MeV/C^2$ - $p = m v = 0.5 MeV(\frac{v}{C^2})$ </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Importance of this extension $\rightarrow$ Electron Diffraction $\rightarrow$ <span style = "color:blue"> Electron </span> $\rightarrow$ Wave $\rightarrow$ Bragg Diffraction Condition </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Wave </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - Wave the nature of electrons can be seen in diffraction from crystals. </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">Electron Diffraction $\rightarrow$ Electron $\rightarrow$ <span style = "color:blue"> Wave </span> $\rightarrow$ Bragg Diffraction Condition $\rightarrow$ Constructive Interference </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Bragg Diffraction Condition </primary> <hr> <main> <div style='float: left; width:50%;text-align:left;font-size:30px'> - $n \lambda=2 d \sin \theta$ </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/14e65e61-d0d8-4bab-0d12-65c493e4d100/public" width="60%" > <!----> </main> <hr> <footer style = "font-size: 18px">Electron $\rightarrow$ Wave $\rightarrow$ <span style = "color:blue"> Bragg Diffraction Condition </span> $\rightarrow$ Constructive Interference $\rightarrow$ The Experimentalists </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Constructive Interference </primary> <hr> <main> <div style='float: left; width:50%;text-align:left;font-size:30px'> - $2d\sin \theta = n \lambda$ - Constructive interference - $n \rightarrow$ integer </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/f0adb382-3936-4da8-e367-7edf637fec00/public" width="70%" > <!----> </main> <hr> <footer style = "font-size: 18px">Wave $\rightarrow$ Bragg Diffraction Condition $\rightarrow$ <span style = "color:blue"> Constructive Interference </span> $\rightarrow$ The Experimentalists $\rightarrow$ Year of Experiment </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> The Experimentalists </primary> <hr> <main> <div style='float: left; width:50%;text-align:left;font-size:30px'> - **Davisson and Germer** </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/4907c5b2-c917-455d-2e35-5529a7430200/public" width="50%"> </main> <hr> <footer style = "font-size: 18px">Bragg Diffraction Condition $\rightarrow$ Constructive Interference $\rightarrow$ <span style = "color:blue"> The Experimentalists </span> $\rightarrow$ Year of Experiment $\rightarrow$ The Experiment </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Year of Experiment </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - 1924 $\longrightarrow$ Matter Wave hypothesis - 1927 $\longrightarrow$ Verified on $Ni$ crystal - 1928 </div> <div style='float: right; width:00%;'> <!----> </main> <hr> <footer style = "font-size: 18px">Constructive Interference $\rightarrow$ The Experimentalists $\rightarrow$ <span style = "color:blue"> Year of Experiment </span> $\rightarrow$ The Experiment $\rightarrow$ The Davisson Germer Apparatus </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> The Experiment </primary> <hr> <main> <div style='float: left; width:50%;text-align:left;font-size:30px'> - **Schematics: NCERT** - **Schematic diagram of apparatus** </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/3f75df4b-c79c-4251-6d2a-ccd4edab0700/public" width="60%" > <!----> <!----> </div> </main> <hr> <footer style = "font-size: 18px">The Experimentalists $\rightarrow$ Year of Experiment $\rightarrow$ <span style = "color:blue"> The Experiment </span> $\rightarrow$ The Davisson Germer Apparatus $\rightarrow$ De Broglie hypothesis </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> The Davisson Germer Apparatus </primary> <hr> <main> <div style='float: right; width:100%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/dbaea716-1909-4c5c-287c-0c9a08b25f00/public" width="40%" > </main> <hr> <footer style = "font-size: 18px">Year of Experiment $\rightarrow$ The Experiment $\rightarrow$ <span style = "color:blue"> The Davisson Germer Apparatus </span> $\rightarrow$ De Broglie hypothesis $\rightarrow$ De Broglie hypothesis </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> De Broglie hypothesis </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $\frac{p^2}{2 m}=e V $ - $p=\sqrt{(2 m e)V} $ - $=k \sqrt{V}=\frac{h}{\lambda} $ - $\lambda=\frac{h}{k \sqrt{V}} \rightarrow \text { hypothesis } $ </div> <div style='float: right; width:00%;'> <!----> </main> <hr> <footer style = "font-size: 18px">The Experiment $\rightarrow$ The Davisson Germer Apparatus $\rightarrow$ <span style = "color:blue"> De Broglie hypothesis </span> $\rightarrow$ De Broglie hypothesis $\rightarrow$ The Davisson Germer Experiment </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> De Broglie hypothesis </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $\lambda =\frac{h}{k \sqrt{V}} $ - $n \lambda=2 d \sin ^2 \theta $ - $=n\frac{h}{k \sqrt{V}} $ </div> <div style='float: right; width:0%;'> <!----> </main> <hr> <footer style = "font-size: 18px">The Davisson Germer Apparatus $\rightarrow$ De Broglie hypothesis $\rightarrow$ <span style = "color:blue"> De Broglie hypothesis </span> $\rightarrow$ The Davisson Germer Experiment $\rightarrow$ X Ray diffraction </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> The Davisson Germer Experiment </primary> <hr> <main> <!--<div style='float: left; width:50%;text-align:left;font-size:30px'>--> <!--</div>--> <div style='width:100%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/fe5c57a9-56ca-4aad-ce25-b94ea0eee400/public"> <!----> </div> </main> <hr> <footer style = "font-size: 18px">De Broglie hypothesis $\rightarrow$ De Broglie hypothesis $\rightarrow$ <span style = "color:blue"> The Davisson Germer Experiment </span> $\rightarrow$ X Ray diffraction $\rightarrow$ More Subtle Matters </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> X Ray diffraction </primary> <hr> <main> <div style='float: left; width:50%;text-align:left;font-size:30px'> - **The diffraction of Cu crystal** </div> <div style='float: right; width:50%;'> <img src="https://imagedelivery.net/YfdZ0yYuJi8R0IouXWrMsA/04477166-e32e-46dd-5393-540080337500/public" width="60%" > <!----> </main> <hr> <footer style = "font-size: 18px">De Broglie hypothesis $\rightarrow$ The Davisson Germer Experiment $\rightarrow$ <span style = "color:blue"> X Ray diffraction </span> $\rightarrow$ More Subtle Matters $\rightarrow$ Relationship between Frequency, Wavelength and Velocity </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> More Subtle Matters </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - What is the frequency? - What is the relationship between frequency, wavelength and the speed? </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">The Davisson Germer Experiment $\rightarrow$ X Ray diffraction $\rightarrow$ <span style = "color:blue"> More Subtle Matters </span> $\rightarrow$ Relationship between Frequency, Wavelength and Velocity $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Relationship between Frequency, Wavelength and Velocity </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> - $p=m v=\frac{h}{\lambda} $ - $E=\frac{p^2}{2 m}= {h \nu} ? $ - $v=\frac{p}{m}=\nu \lambda ?$ </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">X Ray diffraction $\rightarrow$ More Subtle Matters $\rightarrow$ <span style = "color:blue"> Relationship between Frequency, Wavelength and Velocity </span> $\rightarrow$ Thank You $\rightarrow$ </footer>

### <Success style="font-size:25px"> Wave Nature Of Matter L-3 </Success> ### <primary style="font-size:24px"> Thank You </primary> <hr> <main> <div style='float: left; width:100%;text-align:left;font-size:30px'> </div> <div style='float: right; width:0%;'>  </main> <hr> <footer style = "font-size: 18px">More Subtle Matters $\rightarrow$ Relationship between Frequency, Wavelength and Velocity $\rightarrow$ <span style = "color:blue"> Thank You </span> $\rightarrow$ $\rightarrow$ </footer>