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The French physicist Louis de Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelength lambda of a material particle, its linear momentum p and planck constant h.
λ=hp=hmv
The de Broglie relation implies that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles. The waves associated with particles in motion are called matter waves or de Broglie waves. These waves differ from the electromagnetic waves as they
(i) have lower velocities
(ii) have no electrical and magnetic fields and
(iii) are not emitted by the particle under consideration.
The experimental confirmation of the de Broglie’s relation was obtained when Davisson and Germer, in 1927, observed that a beam of electrons is diffracted by a nickel crystal. As diffraction is a characteristic property of waves, hence the beam of electron behaves as a wave, as proposed by de Broglie.

If a proton, electron and alpha -particle are moving with the same kinetic energy then the order of their de-Broglie’s wavelength is?

A
λp>λe>λα
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B
λα>λp>λe
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C
λα<λp<λe
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D
λe=λp<λα
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Solution

The correct option is C λα<λp<λe
According to de-broglie equation:
λ=h2m K.E

where K.E= kinetic energy of partcile =12mv2
m= mass of particle

If kinetic energy is same for all the three particles, then
λ1m
The greater the mass, lower is the value of wavelength. So alpha particles will have the lowest wavelength as it has the highest mass and electrons will have the highest wavelength. While protons will have a value of wavelength between them.
mα>mp>me
Therefore, the correct answer is λα<λp<λe

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The French physicist Louis de Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behaviour. He proposed the following relationship between the wavelengh λ of a material particle, its linear momentum p and planck constant h. λ=hp=hmv
The de Broglie relation implies that the wavelength of a particle should decrease as its velocity increases. It also implies that for a given velocity heavier particles should have shorter wavelength than lighter particles. The waves differ from the electromagnetic waves as they
(i) have lower velocities
(ii) have no electrical and magnetic fields and
(iii) are not emitted by the particle under consideration.
The experimental confirmation of the de Broglie relation was obtained when Davisson and Germer, in 1927, observed that a beam of electrons is diffron behaves as a wave, as proposed by de Broglie. Wemer Heisenberg considered the limits of how precisely we can measure properties of an electron or other microscopic particle like electron. He determined that there is a fundametal limit of how closely we can measure both position and mometum. The more accurately we measure the mokmentum of a particle, the less accurately we can determine its position. The converse is also true. This is summed up in what we now call the "Heisenberg uncertainty principle; It is impossible to determine simultanously and precisely both the momentum and position of a particle. The product of uncertainty in the position, Δx and the uncertainty in the momentum Δ(mv) must be greater than or equal to h4π i.e. ΔxΔ(mv)h4π.
The correct order of wavelength of hydrogen (1H1), Deuterium (1H2) and Tritium(1H3) moving with same kinetic energy is ::
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