Question
Explain the de-Broglie wavelength by explaining the waveform of matter.
✓
Answer
→Some phenomena associated with light like diffraction, interference and polarisation show that light (radiation) has a wave-form.
→Similarly, the photoelectric effect, the Compton effect, show that light has a particle-form.
→Thus, radiation has dual nature.
→The first scientist named Louis de-Broglie questioned whether the universe had symmetry, so if radiation (energy) could act as a particle, then a particle could also act as radiation. If radiation can have dual nature then particle can also have dual nature.
→de-Broglie stated that when a particle (such as an electron, proton etc) moves, it moves in a wave-form.
→de-Broglie said that if a particle has mass $m$ and is moving with speed $v$, then the wave length of the wave of the particle can be given by the formula
$\lambda=\frac{h}{p}=\frac{h}{m v}$
→This wave length is called the de-Broglie wave length of the particle. The above equation is known as the de-Broglie relation.
→The wave length of a photon of radiation, $\lambda=\frac{c}{\nu} \quad(\because c=v \lambda)$
$\lambda=\frac{h}{p} \quad$ (momentum $p=\frac{h v}{c} \therefore \frac{c}{v}=\frac{h}{p}$ )
Thus, the de-Broglie wave length and the wave length of a photon of radiation can be given by the same formula.
→The de-Broglie wave length $\lambda=\frac{h}{p}$.
→In this equation, the physical quantity on the left is wave form and the momentum ( $p$ ) on the right side is the physical quantity of the particle form. Thus this equation relates the wave nature and the particle nature.
→Davisson and Germer's experiment proved deBroglie's hypothesis experimentally.
→Similarly, the photoelectric effect, the Compton effect, show that light has a particle-form.
→Thus, radiation has dual nature.
→The first scientist named Louis de-Broglie questioned whether the universe had symmetry, so if radiation (energy) could act as a particle, then a particle could also act as radiation. If radiation can have dual nature then particle can also have dual nature.
→de-Broglie stated that when a particle (such as an electron, proton etc) moves, it moves in a wave-form.
→de-Broglie said that if a particle has mass $m$ and is moving with speed $v$, then the wave length of the wave of the particle can be given by the formula
$\lambda=\frac{h}{p}=\frac{h}{m v}$
→This wave length is called the de-Broglie wave length of the particle. The above equation is known as the de-Broglie relation.
→The wave length of a photon of radiation, $\lambda=\frac{c}{\nu} \quad(\because c=v \lambda)$
$\lambda=\frac{h}{p} \quad$ (momentum $p=\frac{h v}{c} \therefore \frac{c}{v}=\frac{h}{p}$ )
Thus, the de-Broglie wave length and the wave length of a photon of radiation can be given by the same formula.
→The de-Broglie wave length $\lambda=\frac{h}{p}$.
→In this equation, the physical quantity on the left is wave form and the momentum ( $p$ ) on the right side is the physical quantity of the particle form. Thus this equation relates the wave nature and the particle nature.
→Davisson and Germer's experiment proved deBroglie's hypothesis experimentally.
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