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Debroglie wavelength - (Concept)
De-broglie wavelength
(1) de-Broglie proposed that just like light, matter should exhibit both particle and wave-like properties. This means that just as the photon has momentum as well as wavelength, electrons should also have momentum as well as wavelength, and he proposed the following mathematical relationship:
where m is the mass of the particle, v its velocity, p its momentum,
KE is the Kinetic Energy of the particle,
V is the voltage across which the Charged particle having charge q is accelerated.
(2) de Broglie’s prediction was confirmed experimentally when it was found that an electron beam undergoes diffraction, a phenomenon characteristic of waves.
(3) It needs to be noted that according to de Broglie, every object in motion has a wave character. This wavelength is quite significant for the subatomic particles which have very small masses. The wavelengths associated with ordinary objects are however so short that their wave properties cannot be detected as they have large masses.
(4) Bohr's model and the de Broglie's relation : Number of standing waves made by an electron in nth Bohr orbit
According to Bohr's model,
According to de Broglie's Relation ,
Combining the two
So, the number of waves made by any electron in the nth orbit is equal to the principal quantum number of the orbit i.e. n.
| Exam | Chapter |
| JEE MAIN | Atomic Structure |
The de-Broglie wavelength of a particle of mass 6.63 g moving with a velocity of 100 ms-1 is:
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Calculate the wavelength (in nanometre) associated with a proton moving at 1.0 x 103 ms-1 (Mass of proton = 1.67 × 10-27 kg and h = 6.63 × 10-34 Js)
| A. |
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A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h/λ (where λ is wavelength associated with electron wave) is given by
| A. |
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| D. |
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What is the work function (in eV) of the metal if the light of wavelength generates photoelectrons of velocity
from it ?
(Mass of electron =
Velocity of light =
Planck's constant =
Charge of electron = )
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| B. |
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| C. |
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| D. |
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The de Broglie wavelength () associated with a photoelectron varies with the frequency (
) of the incident radiation as, [
is threshold frequency] :
| A. |
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| B. |
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| C. |
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| D. |
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Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
(a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in orbital of lower angular momentum.
(b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.
(c) According to wave mechanics, the ground state angular momentum is equal to .
(d) The plot of for various azimuthal quantum numbers, shows peak shifting towards higher r-value.
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The de-Broglie’s wavelength of electron present in first Bohr orbit of ‘H’ atom is :
| A. |
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| B. |
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| C. |
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| D. |
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The de Broglie wavelength of an electron in the 4th Bohr orbit is:
| A. |
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| B. |
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| C. |
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| D. |
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The de Broglie wavelength of a car of mass and velocity
is :
| A. |
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| B. |
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| C. |
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| D. |
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A proton and a nucleus are accelerated by the same potential. If
and
denote the de Broglie wavelength of
and proton respectively, then the value of
is
. The value of x______ (Rounded off to the nearest integer).
[Mass of = 8.3 mass of proton]
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| B. |
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| D. |
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A cricket ball of is moving with a velocity of
. The wavelength associated with motion is
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| C. |
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| D. |
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When light of wavelength 248 nm falls on a metal of threshold energy 3.0 eV, the de-Broglie wavelength of emitted electrons is _______. (Round off to the Nearest Integer).
| A. |
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| B. |
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| C. |
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| D. |
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The wavelength of an electron and a neutron will become equal when the velocity of the electron is times the velocity of neutron. The value of
is ___________ . (Nearest Integer)
| A. |
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| B. |
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| C. |
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| D. |
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The wavelength of electrons accelerated from rest through a potential difference of is
.
The value of is _________(Nearest integer)
Given : Mass of electron
Charge on an electron
Planck's constant
| A. |
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| B. |
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| C. |
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| D. |
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If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He+ is :
| A. |
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| B. |
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| C. |
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| D. |
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For a hypothetical H like atom which follows Bohr’s model, some spectral lines were observed as shown. If it is known that line ‘E’ belongs to the visible region, then the lines possibly belonging to the ultraviolet region will be (n1 is not necessarily ground state)
[Assume for this atom, no spectral series shows overlaps with other series in the emission spectrum]
| A. |
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| C. |
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| D. |
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The energy of one quantum of light with a wavelength of 6500(1 = 10-10m) is:
| A. |
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| B. |
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| C. |
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| D. |
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The energy of a photon in Joules that has a wavelength of 9.0m is:
| A. |
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| B. |
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| C. |
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| D. |
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The de Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 metres per second is approximately
| A. |
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| C. |
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| D. |
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The de-Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 metres per second is approximately:
| A. |
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| B. |
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| C. |
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| D. |
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Calculate the wavelength (in nanometre) associated with a proton moving at 1.0 x 103 ms-1.
(Mass of proton = 1.67 × 10-27kg and h = 6.63 × 10-34 Js)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Following figure shows spectrum of an ideal black body at four different temperatures. The number of correct statement/s from the following is________________.
B. The black body consists of particles performing simple harmonic motion.
C. The peak of the spectrum shifts to shorter wavelength as temperature increases.
E. The given spectrum could be explained using quantisation of energy.
| A. |
|
| B. |
|
| C. |
|
| D. |
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The shortest wavelength of a hydrogen atom in the Lyman series is . The longest wavelength in the Balmer series
is
| A. |
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| B. |
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| C. |
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| D. |
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Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from to
of
spectrum
| A. |
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| B. |
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| D. |
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Electrons in a cathode ray tube have been emitted with a velocity of . The number of following statements which is/are true about the emitted radiation is
Given : .
(A) The de Broglie wavelength of the electron emitted is .
(B) The characteristic of electrons emitted depends upon the material of the electrodes of the cathode ray tube.
(C) The cathode rays start from the cathode and move toward the anode.
(D) The nature of the emitted electrons depends on the nature of the gas present in the cathode ray tube.
| A. |
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| B. |
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| C. |
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| D. |
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The wavelength of an electron of kinetic energy 4.50 × 10–29 J is _________ × 10–5 m. (Nearest integer)
Given: mass of electron is 9 × 10–31 kg, h = 6.6 × 10–34 Js
| A. |
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| B. |
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| C. |
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| D. |
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Which of the followings can be concluded from the de-Broglie relationship?
| A. |
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| B. |
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| C. |
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| D. |
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According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron $(\lambda)$ and momentum of electron(p) ?
| A. |
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| B. |
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| C. |
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| D. |
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The French physicist, de Broglie, in 1924 proposed that matter, like radiation, should also exhibit dual behavior i.e., both particle and wavelike properties. This means that just as the photon has momentum as well as wavelength, electrons should also have momentum as well as wavelength, de Broglie, from this analogy, gave the following relation between wavelength (λ) and momentum (p) of a material particle.
