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The Uncertainty Principle

Which of the ...

Question

Which of the following is the best definition of the uncertainty principle?

A

We cannot know for certain when any given radioactive particle will undergo decay

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B

We cannot know both the momentum and the position of a particle at the same time

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C

The laws of physics are the same in all intertial reference frames

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D

Light exhibits both wave and particle properties

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E

An unobserved particle can be in two places at the same time

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Solution

The correct option is B We cannot know both the momentum and the position of a particle at the same time
According to Heisenberg uncertainty principle, the position and velocity (hence, momentum) cannot both be measured exactly, at the same time.

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Q. Assertion :Heisenberg's uncertainity principle is contradictory to Bohr's theory. Reason: The Heisenberg's uncertainty principle states that we can never simultaneously know the exact position and the exact speed of an object. Because everything in the universe behaves like both a particle and a wave at the same time

Q. When a nucleus at rest emits a beta particle, it is found that the velocities of the recoiling nucleus and the beta particle are not along the same straight line. How can this be possible in view of the principle of conservation of momentum?

Q. The uncertainty in position of a particle is same as it's de Broglie wavelength, uncertainty in its momentum is _______

Q. If uncertainty in position and momentum of a particle are numerically equal, then the uncertainty in the speed of the particle should 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}

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 ::

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