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Heisenberg's Uncertainty Principle

The uncertain...

Question

The uncertainty principle and the concept of the wave nature of matter were proposed by _and ___ respectively.
1. De Broglie, Heisenberg
2. Heisenberg; de Broglie
3. Heisenberg; Einstein
4. Einstein; de Broglie

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Solution

In 1927, Werner Heisenberg presented a principle known as Heisenberg uncertainty principle which states as : "It is impossible to measure simultaneously the exact position and exact momentum of a body as small as an electron."
In 1924. a French physicist, Louis De Broglie suggested that if the nature of light is both that of a particle and of a wave, then this dual behavior should be true for the matter also.

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Q. Assuming Heisenberg Uncertainty Principle to be true, what could be the maximum uncertainty in the de-Broglie wavelength of a moving electron accelerated by a potential difference of 6 V whose uncertainty in position is

\frac{7}{22}

Q. De Broglie proposed the wave nature of electrons suggesting matter waves.
Find the momentum, speed and De-Broglie wavelength of an electron with Kinetic energy of

120 e V

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}

Δ x Δ (m v) \geq \frac{h}{4 π}

The correct order of wavelength of hydrogen

(_{1} H^{1})

(_{1} H^{2})

(_{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}

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.

The wavelength of matter waves associated with a body of mass

1000 g

moving with a velocity of

100 m / s e c

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.

Wave nature of electrons is shown by:

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