DUAL NATURE OF RADIATION and MATTER

Dual Nature of Radiation and Matter

  • Wave-Particle Duality: The concept that every particle or quantum entity, such as an electron or photon, may be partly described in terms not only of particles but also of waves.
Join Our Study Groups

de Broglie Wavelength

\[ \lambda = \frac{h}{p} \]

Properties & Key Points:

  • \( \lambda \): Wavelength associated with the particle.
  • \( h \): Planck's constant (\( h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \)).
  • \( p \): Momentum of the particle (\( p = mv \)).
Join Our Study Groups

Energy of Photon

\[ E = h \nu \]

Properties & Key Points:

  • \( E \): Energy of the photon.
  • \( h \): Planck's constant.
  • \( \nu \): Frequency of the electromagnetic wave.
Join Our Study Groups

Einstein's Photoelectric Equation

\[ E_k = h \nu - \phi \]

Properties & Key Points:

  • \( E_k \): Kinetic energy of the emitted electron.
  • \( h \): Planck's constant.
  • \( \nu \): Frequency of the incident light.
  • \( \phi \): Work function (minimum energy required to release an electron).
Join Our Study Groups

Threshold Frequency

\[ \nu_0 = \frac{\phi}{h} \]

Properties & Key Points:

  • \( \nu_0 \): Threshold frequency.
  • \( \phi \): Work function.
  • \( h \): Planck's constant.
Join Our Study Groups

de Broglie Wavelength of Electron in Bohr Orbit

\[ \lambda = \frac{h}{mv} \]

Properties & Key Points:

  • \( \lambda \): Wavelength associated with the electron.
  • \( h \): Planck's constant.
  • \( m \): Mass of the electron.
  • \( v \): Velocity of the electron in the orbit.
Join Our Study Groups

Heisenberg's Uncertainty Principle

\[ \Delta x \Delta p \geq \frac{h}{4 \pi} \]

Properties & Key Points:

  • \( \Delta x \): Uncertainty in position.
  • \( \Delta p \): Uncertainty in momentum.
  • \( h \): Planck's constant.
Join Our Study Groups

Compton Shift

\[ \Delta \lambda = \frac{h}{m_e c} (1 - \cos \theta) \]

Properties & Key Points:

  • \( \Delta \lambda \): Change in wavelength.
  • \( h \): Planck's constant.
  • \( m_e \): Rest mass of the electron.
  • \( c \): Speed of light.
  • \( \theta \): Angle of scattering.
Join Our Study Groups

Energy-Mass Equivalence

\[ E = mc^2 \]

Properties & Key Points:

  • \( E \): Energy.
  • \( m \): Mass.
  • \( c \): Speed of light.
Join Our Study Groups

Rydberg's Formula for Hydrogen Spectrum

\[ \nu = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Properties & Key Points:

  • \( \nu \): Frequency of emitted or absorbed radiation.
  • \( R_H \): Rydberg constant (\( R_H = 1.097 \times 10^7 \, \text{m}^{-1} \)).
  • \( n_1, n_2 \): Principal quantum numbers of the electron's orbit.
Join Our Study Groups