Shortcut Methods
Shortcuts and tricks to solve numerical problems on the wave nature of matter for JEE and CBSE Board Exams
1️⃣ Wavelength and frequency:
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The speed of light is (3\times10^8) m/s.
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The wavelength ((\lambda)) of a wave is inversely proportional to its frequency ((f)):
- (\lambda = \frac{c}{f})
2️⃣ de Broglie wavelength for particles:
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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
- (\lambda = \frac{h}{p})
where:
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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
- (\Delta y = \frac{\lambda L}{d})
where:
