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The de -Broglie wave corresponding to a particle of mass m and velocity v has a wavelength associated with it [1989]
- a)h/mv
- b)hmv
- c)mh/v
- d)m/hv
Correct answer is option 'A'. Can you explain this answer?
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De-Broglie wavelength 
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De-Broglie Wavelength Formula:
The de-Broglie wavelength associated with a particle of mass m and velocity v is given by the formula:
λ = h / mv
where:
λ = de-Broglie wavelength
h = Planck's constant
m = mass of the particle
v = velocity of the particle
Explanation:
- The de-Broglie wavelength is a concept in quantum mechanics that describes the wave nature of particles.
- According to de-Broglie, every moving particle has an associated wavelength.
- The formula for calculating the de-Broglie wavelength of a particle is λ = h / mv.
- Here, h is Planck's constant, a fundamental constant of nature, with a value of approximately 6.626 x 10^-34 joule seconds.
- The mass of the particle (m) and its velocity (v) are also taken into account in the formula.
- The de-Broglie wavelength is inversely proportional to the momentum of the particle, which is given by mv.
- As the momentum of the particle increases (higher mass or velocity), the de-Broglie wavelength decreases, indicating a more particle-like behavior.
- Conversely, as the momentum decreases, the de-Broglie wavelength increases, indicating a more wave-like behavior.
Therefore, the correct formula for the de-Broglie wavelength associated with a particle of mass m and velocity v is λ = h / mv.
The de-Broglie wavelength associated with a particle of mass m and velocity v is given by the formula:
λ = h / mv
where:
λ = de-Broglie wavelength
h = Planck's constant
m = mass of the particle
v = velocity of the particle
Explanation:
- The de-Broglie wavelength is a concept in quantum mechanics that describes the wave nature of particles.
- According to de-Broglie, every moving particle has an associated wavelength.
- The formula for calculating the de-Broglie wavelength of a particle is λ = h / mv.
- Here, h is Planck's constant, a fundamental constant of nature, with a value of approximately 6.626 x 10^-34 joule seconds.
- The mass of the particle (m) and its velocity (v) are also taken into account in the formula.
- The de-Broglie wavelength is inversely proportional to the momentum of the particle, which is given by mv.
- As the momentum of the particle increases (higher mass or velocity), the de-Broglie wavelength decreases, indicating a more particle-like behavior.
- Conversely, as the momentum decreases, the de-Broglie wavelength increases, indicating a more wave-like behavior.
Therefore, the correct formula for the de-Broglie wavelength associated with a particle of mass m and velocity v is λ = h / mv.
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