physics-class-12-unit-11-chapter-01-photoelectric-effect-einsteins-explanation-l-1-5-pi1ijbiqebm

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Important Features </primary>
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- Intensity - Frequency interplay

- Minimum frequency required for photoemission
- Proportional to Intensity beyond the minimum frequency
- No emission below the minimum frequency
- Linear Relation between the frequency and the stopping potential

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<footer style = "font-size: 18px">Photoelectric Effect Einstein's Explanation $\rightarrow$ Millikan Experiment $\rightarrow$ <span style = "color:blue"> Important Features </span> $\rightarrow$ Photoelectric Effect $\rightarrow$ Experiment </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Experiment </primary>
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- No emission takes place if $\nu < \nu_{\min}$

- Radiation of frequency $\nu$ is equivalent to a collection of quanta, each of which carries an energy $h \nu$.

- $U_{c l} =\frac{\varepsilon_0}{2} \vec{E}_0^2 $

- $U_{P E} =n_{p h}\{h \nu\}$

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<footer style = "font-size: 18px">Important Features $\rightarrow$ Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Experiment </span> $\rightarrow$ Experiment $\rightarrow$ Planck Hypothesis </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Problems and Motivations </primary>
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- **Paradigm Shift**

- Maxwell Equations imply Wave Nature

- $\rightarrow$ Energy spread continuously in space

- $\rightarrow$ Confirmed by Experiments

- Photon means particle nature of light

- $\rightarrow$ Energy and momentum are distributed discontinuously in space

- Justification

- Temporal scales!

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<footer style = "font-size: 18px">Classical Fields $\rightarrow$ Capacitor $\rightarrow$ <span style = "color:blue"> Problems and Motivations </span> $\rightarrow$ Wave Nature Seen Over Large Temporal Scales $\rightarrow$ The Einstein Hypothesis </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Wave Nature Seen Over Large Temporal Scales </primary>
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- This is the fundamental observation of Einstien

- The electromagnetic wave is coming that have a frequency of

- $\nu = 10^{14} hz$
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<footer style = "font-size: 18px">Capacitor $\rightarrow$ Problems and Motivations $\rightarrow$ <span style = "color:blue"> Wave Nature Seen Over Large Temporal Scales </span> $\rightarrow$ The Einstein Hypothesis $\rightarrow$ The Einstein Hypothesis </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> The Einstein Hypothesis </primary>
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- **Photons are for Real**

- **Two simple but radical assumptions**

- The incident radiation of frequency $\nu$ can be looked upon as a stream of photon "gas" with each photon carrying an energy $h \nu$
- Electrons in the metal escape to free space by transfer of energy from an individual photon
- Energy is strictly conserved in this process
- Maximum kinetic energy corresponds to complete absorption of photon

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<footer style = "font-size: 18px">Problems and Motivations $\rightarrow$ Wave Nature Seen Over Large Temporal Scales $\rightarrow$ <span style = "color:blue"> The Einstein Hypothesis </span> $\rightarrow$ The Einstein Hypothesis $\rightarrow$ The Einstein Hypothesis </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> The Einstein Hypothesis </primary>
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- $\Phi = 3 eV$

- $\nu_{\min} = \frac{\Phi}{h}$

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<footer style = "font-size: 18px">Wave Nature Seen Over Large Temporal Scales $\rightarrow$ The Einstein Hypothesis $\rightarrow$ <span style = "color:blue"> The Einstein Hypothesis </span> $\rightarrow$ The Einstein Hypothesis $\rightarrow$ Explanation of the Millikan Results </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> The Einstein Hypothesis </primary>
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<footer style = "font-size: 18px">The Einstein Hypothesis $\rightarrow$ The Einstein Hypothesis $\rightarrow$ <span style = "color:blue"> The Einstein Hypothesis </span> $\rightarrow$ Explanation of the Millikan Results $\rightarrow$ Reconciliation with Millikan </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Explanation of the Millikan Results </primary>
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- **Simple and elegant**

- Let the work function of an electron be $\phi_0$
- $\phi_0$ is the minimum energy required to emit an electron by irradiation
- Electrons completely absorb a photon for their emission (Einstein)
- Each photon carries an energy $h \nu$ (Planck)

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<footer style = "font-size: 18px">The Einstein Hypothesis $\rightarrow$ The Einstein Hypothesis $\rightarrow$ <span style = "color:blue"> Explanation of the Millikan Results </span> $\rightarrow$ Reconciliation with Millikan $\rightarrow$ Energy of the Photon </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Reconciliation with Millikan </primary>
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- $E_i=h \nu$
- $E_f=E_{k i n}^{\max }+\phi_0$
- $h \nu=h \nu_0+E_{k i n}^{\max }$

- The Lenard-Millikan Result

- $h\left(\nu-\nu_0\right)=E_{\text {kin }}^{\max } \equiv e \times($ Stopping potential)

- $E_i^{photon}=h \nu ; \quad E_i^e=0$

- $E_f^{tot}=E_{kin }^{max}+\Phi_0$

- $h(\nu-\nu_0)=E_{kin }^{min} h \nu_0$
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<footer style = "font-size: 18px">The Einstein Hypothesis $\rightarrow$ Explanation of the Millikan Results $\rightarrow$ <span style = "color:blue"> Reconciliation with Millikan </span> $\rightarrow$ Energy of the Photon $\rightarrow$ Relativity </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Relativistic Momentum </primary>
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- $m_0 \rightarrow 0$

- $C_0 \rightarrow \infty $

- $m_0 = 0 \Rightarrow \varepsilon = p = 0$

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

- $v = c \Rightarrow \varepsilon = p = \infty $

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

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<footer style = "font-size: 18px">Momentum Density $\rightarrow$ Relativistic Momentum $\rightarrow$ <span style = "color:blue"> Relativistic Momentum </span> $\rightarrow$ Relativistic Momentum $\rightarrow$ Particles Relativistic </footer>

### <Success style="font-size:25px"> Photoelectric Effect Einsteins Explanation L-1 </Success>
### <primary style="font-size:24px"> Particles Relativistic </primary>
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- $\varepsilon = \frac{m_0 c^2}{\sqrt{1-v^2 / c^2}}$

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

- $\varepsilon^2 = \frac{m_0 c^4}{\sqrt{1-v^2 / c^2}}$

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

- $\varepsilon^2 = m_0^2 c^4 + p_0^2 c^2$

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<footer style = "font-size: 18px">Relativistic Momentum $\rightarrow$ Particles Relativistic $\rightarrow$ <span style = "color:blue"> Particles Relativistic </span> $\rightarrow$ Particles Relativistic $\rightarrow$ Rayleigh scattering </footer>