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Zorluk: KolayWave-Particle Duality and de Broglie Wavelength

According to de Broglie's hypothesis on wave-particle duality, how does the de Broglie wavelength of a moving particle change if its momentum is doubled?

  1. A
    It is doubled
  2. It is halvedCevap
  3. C
    It is quadrupled
  4. D
    It remains unchanged

Cevap

The de Broglie wavelength is halved when the momentum of the particle is doubled.
By de Broglie's equation λ=hp\lambda = \frac{h}{p}, the wavelength λ\lambda is inversely proportional to momentum pp. Doubling the momentum replaces pp with 2p2p, resulting in a new wavelength of h2p=λ2\frac{h}{2p} = \frac{\lambda}{2}, which means the wavelength is halved.

Adım Adım Çözüm

1
State the de Broglie wavelength formula
λ=hp\lambda = \frac{h}{p}
The de Broglie wavelength λ\lambda is inversely proportional to particle momentum pp.
2
Substitute doubled momentum p′=2pp' = 2p into the formula
λ′=h2p=12λ\lambda' = \frac{h}{2p} = \frac{1}{2}\lambda
Increasing momentum by a factor of 2 scales the wavelength by 12\frac{1}{2}.

Anahtar Kavram

Inverse proportionality between de Broglie wavelength and particle momentum
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Wave-Particle Duality and de Broglie Wavelength

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