Dual Nature of Radiation and Matter PDF

## Threshold Wavelength The maximum wavelength (longest wavelength) of incident radiation which can cause photoelectric effect. **Formula:** - **E ≥ Φ** - **Φ = hc / λo** - **λo = hc / Φ** - **Kmax = E - Φ** - **Kmax = hc / λ** where: - **E** is the energy of incident radiation (in eV) - *...

## Threshold Wavelength The maximum wavelength (longest wavelength) of incident radiation which can cause photoelectric effect. **Formula:** - **E ≥ Φ** - **Φ = hc / λo** - **λo = hc / Φ** - **Kmax = E - Φ** - **Kmax = hc / λ** where: - **E** is the energy of incident radiation (in eV) - **Φ** is the work function of the metal (in eV) - **λo** is the threshold wavelength (in nm) - **hc** is Planck's constant multiplied by the speed of light (1240 eV nm) - **Kmax** is the maximum kinetic energy of the emitted electron (in eV) - **λ** is the wavelength of the incident radiation (in nm) ## Photoelectric Effect When there is no collision, the electron comes out of the metal surface most efficiently. **Formula:** * **(K.E.)max = E - Φ** On increasing the intensity of radiation (light), the number of photons increases, but the energy of each photon is still the same. Hence Kmax of the photoelectron remains unaffected, while the intensity of radiation changes. **Summary of Photoelectric Effect:** * The maximum kinetic energy of the emitted photoelectrons is independent of the intensity of incident light. * The stopping potential is proportional to the frequency of incident light. * For each metal, there exists a certain minimum frequency of light below which no photoelectrons are emitted, no matter how intense the light is. ## Stopping Potential (Vo) The minimum magnitude of negative potential on the anode with respect to the cathode which can just stop the photocurrent. **Formula:** * **Vo = Kmax / e** * **Kmax = E - Φ** * **Vo = (E - Φ) / e** * **Vo = hc / eλ** ## De Broglie Wavelength Every moving particle has a wave associated with it. **Formula:** * **λ = h / p** * ** λ = h / (√2mK.E)** * ** λ = h / (√2mqV)** where: * **λ** is the De Broglie wavelength (in m) * **h** is Planck's constant (6.626 x 10^-34 J s) * **p** is the momentum of the particle (in kg m/s) * **m** is the mass of the particle (in kg) * **K.E.** is the kinetic energy of the particle (in J) * **q** is the charge of the particle (in C) * **V** is the potential difference applied to the particle (in V) ## Summary Table | Concept | Formula | Description | |---|---|---| | Threshold Wavelength | λo = hc / Φ | The maximum wavelength of incident radiation which can cause photoelectric effect. | | Photoelectric Effect | (K.E.)max = E - Φ | The kinetic energy of the emitted photoelectrons is independent of the intensity of incident light. | | Stopping Potential (Vo) | Vo = Kmax / e | The minimum magnitude of negative potential on the anode with respect to the cathode which can just stop the photocurrent. | | De Broglie Wavelength | λ = h / p | Every moving particle has a wave associated with it. |