-
Engineering and Architecture
Exams
Colleges
Predictors
Resources
-
Computer Application and IT
Quick Links
Colleges
-
Pharmacy
Colleges
Resources
-
Hospitality and Tourism
Colleges
Resources
Diploma Colleges
-
Competition
Other Exams
Resources
-
School
Exams
Top Schools
Products & Resources
-
Study Abroad
Top Countries
Resources
-
Arts, Commerce & Sciences
Colleges
Upcoming Events
Resources
-
Management and Business Administration
Exams
Colleges & Courses
Predictors
-
Learn
Law Preparation
MBA Preparation
Engineering Preparation
Medical Preparation
-
Online Courses and Certifications
Top Streams
Specializations
- Digital Marketing Certification Courses
- Cyber Security Certification Courses
- Artificial Intelligence Certification Courses
- Business Analytics Certification Courses
- Data Science Certification Courses
- Cloud Computing Certification Courses
- Machine Learning Certification Courses
- View All Certification Courses
Resources
-
Medicine and Allied Sciences
Colleges
Predictors
Resources
-
Law
Resources
Colleges
-
Animation and Design
Exams
Predictors & Articles
Colleges
Resources
-
Media, Mass Communication and Journalism
Colleges
Resources
-
Finance & Accounts
Top Courses & Careers
Colleges
De broglie 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:
$\lambda=\frac{h}{m v}=\frac{h}{p}=\frac{h}{\sqrt{2 m K E}}=\frac{h}{\sqrt{2 m q V}}$
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,
$m v r=\frac{n h}{2 \pi}$
According to de Broglie's Relation ,
$p=\frac{h}{\lambda}$
Combining the two
$2 \pi r=n \lambda$
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:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
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 = )
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The de Broglie wavelength () associated with a photoelectron varies with the frequency (
) of the incident radiation as, [
is threshold frequency] :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The de-Broglie’s wavelength of electron present in first Bohr orbit of ‘H’ atom is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The de Broglie wavelength of an electron in the 4th Bohr orbit is:
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The de Broglie wavelength of a car of mass and velocity
is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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]
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A cricket ball of is moving with a velocity of
. The wavelength associated with motion is ____ $\times$10−35
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He+ is :
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
The energy of one quantum of light with a wavelength of 6500(1 = 10-10m) is____ x 10-19J
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The energy of a photon in Joules that has a wavelength of 9.0m is ____×10-26
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The de Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 metres per second is approximately
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The de Broglie wavelength of a tennis ball of mass 60g moving with a velocity of 10 meters per second is approximate:(Planck's constant, $\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}$ )
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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) ____nm
| 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________________.
A. $\mathrm{T}_4>\mathrm{T}_3>\mathrm{T}_2>\mathrm{T}_1$
B. The black body consists of particles performing simple harmonic motion.
C. The peak of the spectrum shifts to shorter wavelength as temperature increases.
D. $\frac{T_1}{v_1}=\frac{T_2}{v_2}=\frac{T_3}{v_3} \neq$ constant
E. The given spectrum could be explained using quantisation of energy.
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The shortest wavelength of a hydrogen atom in the Lyman series is . The longest wavelength in the Balmer series
is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from to
of
spectrum
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
Which of the followings can be concluded from the de-Broglie relationship?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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. |
|
| B. |
|
| C. |
|
| D. |
|
The de-Broglie's wavelength of an electron in the $4^{\text {th }}$ orbit is _________$\qquad$ $\pi \mathrm{a}_0 .\left(\mathrm{a}_0=\right.$ Bohr's radius)
| A. |
|
| B. |
|
| C. |
|
| D. |
|
What is de Broglie wavelength (in $10^{-29}$m) associated with particle of mass $10^6 \mathrm{~kg}$ moving a velocity of $10 \mathrm{~cm} / \mathrm{s}$ is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The wavelength of a ball of mass 1kg moving with a velocity of $10 \mathrm{~ms}^{-1}$ ?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A photon of wavelength 6000 Å has an energy E. The wavelength of the photon of light which corresponds to an energy equal to 2E is ____ Å
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If the velocity of the electron in Bohr is the first orbit is 3.78 X 106 m/s. What will be the de Broglie wavelength?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A metal is irradiated with light of wavelength 660 nm. Given that the work function of the metal is 1.0 eV, the de Broglie wavelength (in n x $10^{-9} \mathrm{~m}$) of the ejected electron is close to
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The correct representation of wavelength-intensity relationship of an ideal blackbody radiation at two different temperatures$T_1$ and $T_2$ is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A partical has mass 1 mg and velocity $4.5 \times 10^5 \mathrm{~cm} / \mathrm{sec}_{\text {,}} h=6.62 \times 10^{-27}$.then $\lambda{\text { for partical }}$ will be :---
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A $20 g$ object is moving with velocity $100 \mathrm{~ms}^{-}$. The de Broglie wavelenght (in m ) of the object is ____$ \times 10^{-34}$
[Planck's constant $h=6.626 \times 10^{-34} \mathrm{~J}$ s]
| A. |
|
| B. |
|
| C. |
|
| D. |
|
C60 emerging from a source at a speed (v) has a de Broglie wavelength of 11.0 A. The value of v (in ms-1) is closest to
[ Planck's constant h = 6.626 x 10-34 Js ]
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If $\mathrm{a}_0$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength $(\lambda)$ of the electron present in the second orbit of hydrogen atom? [ n : any integer]
| A. |
|
| B. |
|
| C. |
|
| D. |
|
If traveling at same speeds, which of the following matter waves have the shortest wavelength?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
A photon of light of wavelength 6000$\ A^o$ has energy E. The wavelength of the photon of a light that has energy 4E ____$\ A^o$
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The ratio of root mean square velocity of hydrogen at 50 K to that of nitrogen at 500 K is closest to
| A. |
|
| B. |
|
| C. |
|
| D. |
|
The value of Planck's constant is . The speed of light is
. Which value is closest to the wavelength in nanometer of a quantum of light with frequency of
?
| A. |
|
| B. |
|
| C. |
|
| D. |
|
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.
-
- Atomic Models
- Developments leading to the Bohr’s model of atom
- Particle Nature of electromagnetic radiation
- Photoelectric Effect
- Line Spectrum of hydrogen
- Bohr model for hydrogen atom
- Dual behavior of matter
- Heisenberg’s uncertainty principle
- Elementary ideas of quantum mechanics
- Quantum mechanical model of atom
- Quantum Numbers (Concept)
- Shape of Orbitals (Concept)
- Radial nodes and planar nodes (Concept)
- Aufbau Principle, Pauli Exclusion Principle and Hund's Rule of Maximum Multiplicity (Concept)
- Electronic configuration of any element (Concept)
- Stability of Completely filled and Half-filled Subshells (Concept)
