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De Broglie's Hypothesis

The French ph...

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 wavelength lambda of a material particle, its linear momentum p and planck constant h.
$λ = \frac{h}{p} = \frac{h}{m v}$
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
$(i i)$ have no electrical and magnetic fields and
$(i i i)$ 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?

λ_{p} > λ_{e} > λ_{α}

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λ_{α} > λ_{p} > λ_{e}

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λ_{α} < λ_{p} < λ_{e}

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λ_{e} = λ_{p} < λ_{α}

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Solution

The correct option is C $λ_{α} < λ_{p} < λ_{e}$
According to de-broglie equation:
$λ = \frac{h}{\sqrt{2 m K . E}}$

where $K . E =$ kinetic energy of partcile $= \frac{1}{2} m v^{2}$
$m =$ mass of particle

If kinetic energy is same for all the three particles, then
$λ \propto \frac{1}{\sqrt{m}}$
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.
$m_{α} > m_{p} > m_{e}$
Therefore, the correct answer is $λ_{α} < λ_{p} < λ_{e}$

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Similar questions

Q. 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 = \frac{h}{p} = \frac{h}{m v}

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

(i i)

have no electrical and magnetic fields and

(i i i)

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.

Using Bohr’s theory, the transition, so that the electron's de-Broglie wavelength becomes 3 times of its original value in

H e^{+}

ion will be?

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 = \frac{h}{p} = \frac{h}{m v}

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,

Δ x

and the uncertainty in the momentum

Δ (m v)

must be greater than or equal to

\frac{h}{4 π}

i.e.

Δ x Δ (m v) \geq \frac{h}{4 π}

The correct order of wavelength of hydrogen

(_{1} H^{1})

, Deuterium

(_{1} H^{2})

and Tritium

(_{1} H^{3})

moving with same kinetic energy is ::

Dual nature of matter was proposed by de Broglie in 1923, it was experimentally verified by Davisson and Germer by diffraction experiment. Wave character of matter has significance only for microscopic particles. de Broglie wavelength or wavelength of matter wave can be calculated using the following relation:

λ = \frac{h}{m v}

where, '

m

' and '

v

' are the mass and velocity of the particle. de Broglie hypothesis suggested that electron waves were being diffracted by the target, much as

X

-rays are diffracted by planes of atoms in the crystals.

Planck's constant has same dimension as that of:

λ = \frac{h}{m v}

where, '

m

' and '

v

' are the mass and velocity of the particle. de Broglie hypothesis suggested that electron waves were being diffracted by the target, much as

X

-rays are diffracted by planes of atoms in the crystals.

De-Broglie equation is obtained by combination of which of the following theories?

Dual nature of matter was proposed by de Broglie in 1923, it was
experimentally verified by Davisson and Germer by diffraction
experiment. Wave character of matter has significance only for
microscopic particles. de Broglie wavelength or wavelength of
matter wave can be calculated using the following relation:

λ = \frac{h}{m v}

where, '

m

' and '

v

' are the mass and velocity of the particle.
de Broglie hypothesis suggested that electron waves were being
diffracted by the target, much as

X

-rays are diffracted by planes of
atoms in the crystals.

The wavelength of matter waves associated with a body of mass

1000 g

moving with a velocity of

100 m / s e c

is:

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