Class 12PhysicsDual Nature of Radiation and matterDavisson-Germer Experiment and Heisenberg Uncertainty Principle
DifficultWhat is a wave packet? Explain using a necessary diagram.
(N/A) resultant wave obtained by the superposition of waves of different wavelengths is called a wave packet.
The matter wave associated with an electron is not extended in infinite space. It is a wave packet extended about a central wavelength.
In this condition,$\Delta x$ is not infinite but has a definite value which depends on the range of the wave packet.
Also,a wave packet does not have a definite wavelength but is made up of a number of wavelengths around a central wavelength.
With the description of a wave packet using the de-Broglie relation and Born's probability interpretation,one can reproduce Heisenberg's uncertainty principle exactly.
Figure $(a)$ shows a schematic diagram of a wave packet,and figure $(b)$ shows an extended wave with a fixed wavelength.
The matter wave associated with an electron is not extended in infinite space. It is a wave packet extended about a central wavelength.
In this condition,$\Delta x$ is not infinite but has a definite value which depends on the range of the wave packet.
Also,a wave packet does not have a definite wavelength but is made up of a number of wavelengths around a central wavelength.
With the description of a wave packet using the de-Broglie relation and Born's probability interpretation,one can reproduce Heisenberg's uncertainty principle exactly.
Figure $(a)$ shows a schematic diagram of a wave packet,and figure $(b)$ shows an extended wave with a fixed wavelength.
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Similar Questions
In the Davisson-Germer experiment,an electron beam of energy $60 \ eV$ is incident normally on a crystal surface. If the maximum intensity is observed at an angle of $50^\circ$ with the direction of the incident beam,what is the interatomic spacing in the crystal lattice in $\mathring A$?
Medium
View Solution$A$ sodium atom is in one of the states labeled 'Lowest excited levels'. It remains in that state for an average time of $10^{-8} \, s$,before it makes a transition back to a ground state. What is the uncertainty in energy of that excited state?
Medium
View SolutionThe wave nature of electrons suggests that they will produce diffraction effects. Davisson and Germer experimentally proved this by diffracting electrons from a crystal. The law of diffraction from a crystal is obtained from the constructive interference of electron waves reflected from the planes of atoms in the crystal. Electrons accelerated by a potential $V$ are diffracted by a crystal. If $d = 1 \ \mathring{A}$ and $i = 30^\circ$,then the value of $V$ should be ........... $V$. $(h = 6.6 \times 10^{-34} \ J \cdot s, m_e = 9.1 \times 10^{-31} \ kg, e = 1.6 \times 10^{-19} \ C)$
Medium
View SolutionStatement $1$: The Davisson-Germer experiment established the wave nature of electrons. Statement $2$: If electrons possess wave nature,they can undergo interference and diffraction.
Easy
View SolutionGiven below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ The beam of electrons shows wave nature and exhibits interference and diffraction.
Reason $R:$ Davisson-Germer experimentally verified the wave nature of electrons.
In the light of the above statements,choose the most appropriate answer from the options given below:
Assertion $A:$ The beam of electrons shows wave nature and exhibits interference and diffraction.
Reason $R:$ Davisson-Germer experimentally verified the wave nature of electrons.
In the light of the above statements,choose the most appropriate answer from the options given below:
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