Shortcuts and tricks to solve numerical problems on the wave nature of matter for neet and CBSE Board Exams#

1️⃣ Wavelength and frequency:#

• The speed of light is (3\times10^8) m/s.

• The wavelength ((\lambda)) of a wave is inversely proportional to its frequency ((f)):

  • (\lambda = \frac{c}{f})

2️⃣ de Broglie wavelength for particles:#

• The de Broglie wavelength ((\lambda)) of a particle is given by:

  • (\lambda = \frac{h}{p}) where:
    • (h) is Planck’s constant ((h = 6.626\times10^{-34}) Js)
    • (p) is the momentum of the particle

• The momentum of a particle is given by the product of its mass and velocity.

3️⃣ Interference and diffraction:#

• The distance ((\Delta y)) between the central bright fringe and the first dark fringe in a double-slit interference pattern is given by:
  • (\Delta y = \frac{\lambda L}{d}) where:
    • (\lambda) is the wavelength of the light
    • (L) is the distance from the slits to the screen
    • (d) is the slit separation

Please provide some other shortcuts methods and tricks not mentioned in the numerical exercises above.#