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Quantum Numbers

Dual nature o...

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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:

A

work

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B

energy

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C

power

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D

angular momentum

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Solution

The correct option is C angular momentum
Angular momentum $\Rightarrow m v r = \frac{n h}{2 π}$
has dimention as that of planck's constant.

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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}

m

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}

m

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.

Which among the following is not used to calculate the de Broglie wavelength?

The French physicist Louis de Broglie in 1924 postulated that matter, like radiation, should exhibit a dual behavior. He proposed the following relationship between the wavelength

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 a 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 wave 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 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 proton, electron and

α

-particle are moving with same kinetic energy then the order of their de-Broglie's wavelength.

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^{+}

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