physics-class-12-unit-11-chapter-02-photoelectric-effects-facts-and-prospects-l-2-5-lekcomxymce

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Universality Millikan </primary>
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- $\nu \times e $: maximum Energy

- Slope is a universal constant

- **Universality: Millikan**

- Ack: Millikan + Wiki

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<footer style = "font-size: 18px">Photo electric Effect Time Line $\rightarrow$ 1905- Annus Mirabilis(The Miraculous Year) $\rightarrow$ <span style = "color:blue"> Universality Millikan </span> $\rightarrow$ Important Points $\rightarrow$ The Mystery of Photoelectric Effect </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Important Points </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

- **Universality: Millikan**

- Ack: Millikan + Wiki

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<footer style = "font-size: 18px">1905- Annus Mirabilis(The Miraculous Year) $\rightarrow$ Universality Millikan $\rightarrow$ <span style = "color:blue"> Important Points </span> $\rightarrow$ The Mystery of Photoelectric Effect $\rightarrow$ Monochromatic Plane Wave </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Monochromatic Plane Wave </primary>
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- $\vec{E}=\overrightarrow{E_0} \sin (k Ƶ -\omega t) $

- $U=\epsilon_0 \vec{E}_0^2 $

- $= \epsilon_0 \vec{E}_0^2 \sin ^2(k Ƶ-\omega t) $

- $\langle U\rangle=\frac{\epsilon_0 \vec{E}_0^2}{2}$

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<footer style = "font-size: 18px">Important Points $\rightarrow$ The Mystery of Photoelectric Effect $\rightarrow$ <span style = "color:blue"> Monochromatic Plane Wave </span> $\rightarrow$ The Mystery of Photoelectric Effect $\rightarrow$ Time Scales </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Forced Oscillation </primary>
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- **Time Scales**

- Emission Times Estimate

- $E_{a b s}=\frac{\text { Energy/unit time }}{\text { electron }}=\frac{(U \times c \times \text { Area })}{(\text { Number of electrons })} $

- $T=\frac{\phi_0}{\mathscr{E}}$

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<footer style = "font-size: 18px">The Mystery of Photoelectric Effect $\rightarrow$ Time Scales $\rightarrow$ <span style = "color:blue"> Forced Oscillation </span> $\rightarrow$ Emission Time $\rightarrow$ Example </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Emission Time </primary>
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- Numerical Estimate

- Relevant Data

|  Material | Sodium |
| -------- | -------- |
| Work function     |  $2.36 \mathrm{eV}$     |
| Number of Electrons    | $10^{19}$     |
| Wavelength    | $300-400 \mathrm{~nm}$   |
| Intensity    | $\approx 10^{-6} \mathrm{~W} / \mathrm{m}^2$     |
| Energy/Atom    | $\approx 10^{-25} \mathrm{~W}$     |
| Time taken for emission    | $\approx 2.6 \times 10^6 \mathrm{~s}$     |

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<footer style = "font-size: 18px">Time Scales $\rightarrow$ Forced Oscillation $\rightarrow$ <span style = "color:blue"> Emission Time </span> $\rightarrow$ Example $\rightarrow$ Ordinary Units </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Ordinary Units </primary>
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- **Comparisons**

- Time required for Emission: $\approx$ One Month!!!!!

- Real Time Required: $10^{-9} \mathrm{s}$

- Discrepancy: $10^{15}$ a Huge number

- The Earth-Sun Distance: $10^{11} \mathrm{m}$

- Size of a dust particle: $10^{-5}-10^{-6} \mathrm{m}$
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<footer style = "font-size: 18px">Emission Time $\rightarrow$ Example $\rightarrow$ <span style = "color:blue"> Ordinary Units </span> $\rightarrow$ Crisis in Physics $\rightarrow$ A particle interpretation </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Crisis in Physics </primary>
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- Experiments and Experiments

- Wave Nature of electromagnetic radiation has solid experimental support
- Laws of reflection and refraction (Fresnel)
- Diffraction
- interference

- (1) Young double slit (Visible region - Light)

- (2) Hertz and J C Bose (microwave)

- J C Bose and Marconi (Radio Waves)

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<footer style = "font-size: 18px">Example $\rightarrow$ Ordinary Units $\rightarrow$ <span style = "color:blue"> Crisis in Physics </span> $\rightarrow$ A particle interpretation $\rightarrow$ Prehistory Black Body Radiation </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> New Physics $E = h \nu$ </primary>
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- Light can also exhibit Particle like properties

- $ I(\nu, T) = \frac{2h\nu^3}{c^2} \frac{1}{exp \frac{h\nu}{kT}-1}\longrightarrow (1)$

- Two limits: $h \rightarrow 0$ or $T \rightarrow \infty$

- $I(\nu, T) \rightarrow \frac{2 \nu^2}{c^2 k T} \longrightarrow (2)$

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<footer style = "font-size: 18px">A particle interpretation $\rightarrow$ Prehistory Black Body Radiation $\rightarrow$ <span style = "color:blue"> New Physics $E = h \nu$ </span> $\rightarrow$ Planck Hypothesis $\rightarrow$ Radiation </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Planck Hypothesis </primary>
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- **Prehistory: Black Body Radiation**

- Ultraviolet Catastrophe

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<footer style = "font-size: 18px">Prehistory Black Body Radiation $\rightarrow$ New Physics $E = h \nu$ $\rightarrow$ <span style = "color:blue"> Planck Hypothesis </span> $\rightarrow$ Radiation $\rightarrow$ The Planck Solution </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> The Planck Solution </primary>
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- New Physics: $E = h \nu$

- Light can also exhibit Particle like properties

- $ I(\nu, T) = \frac{2h\nu^3}{c^2} \frac{1}{exp \frac{h\nu}{kT}-1}\longrightarrow (1)$

- Two limits: $h \rightarrow 0$ or $T \rightarrow \infty$

- $I(\nu, T) \rightarrow \frac{2 \nu^2}{c^2 k T} \longrightarrow (2)$
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<footer style = "font-size: 18px">Planck Hypothesis $\rightarrow$ Radiation $\rightarrow$ <span style = "color:blue"> The Planck Solution </span> $\rightarrow$ The Einstein Revolution $\rightarrow$ Marriage of Incompatibles </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Classical- Quantum </primary>
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- $U=\frac{\epsilon_0}{2}\left|\vec{E}_0\right|^2 $

- $U=n_\nu(h \nu) $

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<footer style = "font-size: 18px">The Einstein Revolution $\rightarrow$ Marriage of Incompatibles $\rightarrow$ <span style = "color:blue"> Classical- Quantum </span> $\rightarrow$ The Planck Hypothesis $\rightarrow$ Two Simple but Radical Assumptions </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Two Simple but Radical Assumptions </primary>
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- 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">Classical- Quantum $\rightarrow$ The Planck Hypothesis $\rightarrow$ <span style = "color:blue"> Two Simple but Radical Assumptions </span> $\rightarrow$ Collision $\rightarrow$ Thank You </footer>

### <Success style="font-size:25px"> Photoelectric Effects Facts And Prospects L-2 </Success>
### <primary style="font-size:24px"> Collision </primary>
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- Collision between individual photon & Electron

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<footer style = "font-size: 18px">The Planck Hypothesis $\rightarrow$ Two Simple but Radical Assumptions $\rightarrow$ <span style = "color:blue"> Collision </span> $\rightarrow$ Thank You $\rightarrow$  </footer>