2
Question
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 ::
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 ::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.
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Solution
The correct option is A λH>λD>λT
As we know, λ=hmv=hP=h√2mE
λH=h√2mH×E
λD=h√2×2mH×E
λT=h√2×3mH×E
So,
λH>λD>λT
Hence, te correct option is A
As we know, λ=hmv=hP=h√2mE
λH=h√2mH×E
λD=h√2×2mH×E
λT=h√2×3mH×E
So,
λH>λD>λT
Hence, te correct option is A
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