physics-class-12-unit-12-chapter-04-matter-waves-structure-of-the-atom-l-4-9-a4nc7n4-kqw

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
### <primary style="font-size:24px"> Matter Waves </primary>
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- $ \underline{\underline{\nu}} \quad \underline{\underline{\lambda}} \quad \underline{\underline{v}} $

- $ v=\nu \lambda \text {. } $

- $ E=\underline{\underline{h \nu}} ; \quad \lambda=\frac{h}{p} $

- $ U=\pi c $

- $ \pi = Momentum $

- U = Energy density

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<footer style = "font-size: 18px"> $\rightarrow$ Matter Waves & Structure of Atom $\rightarrow$ <span style = "color:blue"> Matter Waves </span> $\rightarrow$ Matter Waves $\rightarrow$ Massive Particles de Broglie Waves </footer>

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
### <primary style="font-size:24px"> Massive Particles de Broglie Waves </primary>
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- $n \lambda=2 d \sin \theta$

- **Provided we assign**

- $ \lambda = \frac{h}, {p} $ p = known $\lambda = associated $

- <span style="color:green">$ p ; \quad \varepsilon \longrightarrow particle $</span>

- <span style="color:green">$ \nu; \quad\lambda \longrightarrow wave $</span>

- $ \vec{p}=m \vec{v} $

- $ \varepsilon=\frac{1}{2} m v^2=\frac{{p}^2}{2 m} $

- $ v=\nu \lambda $

- $ {v_{\text {par }}} \quad v_{\text {wave }} $

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<footer style = "font-size: 18px">Matter Waves $\rightarrow$ Matter Waves $\rightarrow$ <span style = "color:blue"> Massive Particles de Broglie Waves </span> $\rightarrow$ Angular Frequency $\rightarrow$ Some Problem </footer>

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
### <primary style="font-size:24px"> Angular Frequency </primary>
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- $ E=h \nu=\frac{p^2}{2 m} $

- <span style="color:green">$\nu \rightarrow \underline{\underline{\omega}}$ : angular frequency</span>

- <span style="color:green">$\lambda \rightarrow k \rightarrow$ Wave number  </span>

- $ E=h \nu=h $

- $ \frac{\omega}{2 \pi} = h \omega $

- $ \omega=2 \pi \nu $

- $ p=\frac{h}{\lambda}=\frac{2 \pi \hbar}{\lambda} = h(\frac{2 \pi}{\lambda}) \equiv h k $

- $ \text( \omega, k) \quad v=\nu \lambda $

- <span style="color:green">$ \omega=c k \rightarrow \text{dispersion relation}$ </span>

- $ {\omega}=\underline{\underline{c(k^{\prime}})} k^{\prime} $

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<footer style = "font-size: 18px">Matter Waves $\rightarrow$ Massive Particles de Broglie Waves $\rightarrow$ <span style = "color:blue"> Angular Frequency </span> $\rightarrow$ Some Problem $\rightarrow$ Matter Waves </footer>

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
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<ins>**More subtle matters**</ins>

- What is the frequency?
- What is the relationship between frequency, wavelength and the speed?

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<footer style = "font-size: 18px">Massive Particles de Broglie Waves $\rightarrow$ Angular Frequency $\rightarrow$ <span style = "color:blue"> Some Problem </span> $\rightarrow$ Matter Waves $\rightarrow$ Relativistic Matter Waves </footer>

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
### <primary style="font-size:24px"> Matter Waves </primary>
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- $\lambda_m=\frac{h}{p} ; \nu_m=\frac{E}{h}$

- <ins>Non -relativistic Case</ins>

- $ E=\frac{p^2}{2 m} $

- $ \lambda_m \nu_m=V_{\text {deBroglie}} = (\frac{E}{p}) $

- $ v_{\text {matterwave }} v_{m \omega}=\lambda_{m \omega} v_{m \omega} = \frac{E}{p}=\frac{1}{2} \frac{m v^2}{m v} $

- $ v \rightarrow particle $

- $ =\frac{v}{2} $

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<footer style = "font-size: 18px">Angular Frequency $\rightarrow$ Some Problem $\rightarrow$ <span style = "color:blue"> Matter Waves </span> $\rightarrow$ Relativistic Matter Waves $\rightarrow$ Indian School of Atomism </footer>

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
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- $ E =h \nu ; \quad p=\frac{h}{\lambda} $

- $ \nu =\frac{E}{h} ; \quad \lambda=\frac{h}{p} $

- $ p=\frac{m_0 v}{\sqrt{1-v^2 c^2}} $

- $ v = \underline{\underline{\lambda \nu}} = \frac{E}{p}=\frac{m_0 c^2}{\sqrt{1-v^2 / c^2}} $

- $ v=\frac{E}{p} ; $

- $ E=\frac{m_0 c^2}{\sqrt{1-v^2 / c^2}} $

- $ p=\frac{m_0 v}{\sqrt{1-v / c^2}} $

- $ v_{wave}=\frac{c^2}{v_{\text {particle }}} \quad v<c $

- $ v_{wave} >C $

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-04-Matter-Waves-Structure-of-The-Atom-L-4_9-A4Nc7N4_Kqw-9.jpg)
![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/Physics-Class-12-Unit-12-Chapter-04-Matter-Waves-Structure-of-The-Atom-L-4_9-A4Nc7N4_Kqw-9a.jpg)

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<footer style = "font-size: 18px">Some Problem $\rightarrow$ Matter Waves $\rightarrow$ <span style = "color:blue"> Relativistic Matter Waves </span> $\rightarrow$ Indian School of Atomism $\rightarrow$ Indirect Evidence </footer>

### <Success style="font-size:25px"> Matter Waves Structure Of The Atom L-4 </Success>
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- **<ins>Early Speculations</ins>**

- **India:** Kanada (Vaisheshika School)

- **Greece:** Democritus

- **England:** Isaac Newton, Dalton, ...

- **Other Schools** : The great elements (Greece, India)

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<footer style = "font-size: 18px">Matter Waves $\rightarrow$ Relativistic Matter Waves $\rightarrow$ <span style = "color:blue"> Indian School of Atomism </span> $\rightarrow$ Indirect Evidence $\rightarrow$ A Rigorous Definition </footer>

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- <ins>**Must explain chemical properties**</ins>

- Two major Contenders

- Plum pudding model (Thompson)    
 
- Planetary Model (Rutherford)

- **Figure:** Illustrations of Atomic models

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<footer style = "font-size: 18px">Indirect Evidence $\rightarrow$ A Rigorous Definition $\rightarrow$ <span style = "color:blue"> Models of Atoms </span> $\rightarrow$ Energy $\rightarrow$ Rutherford Scattering </footer>