Class 12 Physics Dual Nature of Radiation and Matter Formulas

• Mass of an Electron

$m_e=9.11\times {10}^{-31}\text{kg}$

• Charge of an Electron

$e=1.602\times {10}^{-19}\text{C}$

• Charge to mass (e/m) Ratio of an Electron

$\frac{e}{m_e}=1.76\times {10}^{11}\text{C/kg}$

• Methods of Emission:
  • Thermionic Emission: When free electrons come out of the metal surface due to a sufficient thermal energy supply.
  • Photoelectric Emission: If electrons are emitted from a metal surface due to illuminating light of suitable frequency.
  • Field Emission: When an electron is forced to come out of the metal surface due to a strong electric field.
• Work function (Φ_o): The minimum energy required for the electron emission from the metal surface.

$${\varphi }_0=h{\nu }_0=\frac{hc}{{\lambda }_0}$$

• Threshold frequency: The minimum cut-off frequency of incident radiation for which photoelectric emission is possible, independent of intensity.

$${\nu }_0=\frac{{\varphi }_0}{h}$$

• Intensity of Light: The number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

$$I=\frac{\text{Power}}{\text{Area}}\text{or}I\propto \text{Number of photons per second}$$

• Saturation Current: The maximum value of the photoelectric current.

$$I_{\text{sat}}\propto \text{Number of photoelectrons emitted per second}\propto \text{Intensity of incident light}$$

• Stopping potential: The minimum negative potential applied to the metal plate for which the photocurrent becomes zero.

$$V_0=\frac{h\nu -{\varphi }_0}{e}$$

• Photoelectric equation: 

$$e{V}_0=K_{\text{max}}=h\nu -{\varphi }_0$$

• Maximum Kinetic Energy:

$$K_{\text{max}}=\frac{1}{2}m{v}^2$$

• Momentum:

$$p\; =\frac{h}{\lambda }=\frac{h\nu }{c}$$

• Energy of photon:  

$$E=h\nu =\frac{hc}{\lambda }$$

•  Number of photons emitted by the source per second: 

$$N = \frac{P}{E} = \frac{P}{h\nu}$$

• De Broglie wavelength of a photon:

$$\lambda =\frac{h}{p}=\frac{h}{mv}$$