Team Quanta gladly presents all possible short questions of Modern Physics & Electronics’ Chapter#02: Wave Particle Duality.
Q.5.1 why is the wave nature of matter not more apparent in our daily observations?
Answer: De-Broglie relation is,
![\[\lambda=\frac{h}{mv}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-4227160ae435aa12b7af7a11afdb0161_l3.png "Rendered by QuickLaTeX.com")
Above equation shows why we do not observe the wave behavior of ordinary objects. Plank’s constant ‘h’ is so small that the wavelength of ordinary objects in many orders of magnitude smaller than the size of a nucleus. No double slit could possibly be constructed on this scale to reveal the wave nature.
Q.5.2 what common expression can be used for momentum of either a photon or a particle?
Answer: The common expression which can be used for the momentum of either a photon or a particle is,
![\[p=\frac{h}{\lambda}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-38e541eb8c90f371363a35e9172d483e_l3.png "Rendered by QuickLaTeX.com")
Where ‘h’ is Plank’s constant.
Q.5.3 If the particles listed below all have same wavelength, which has shortest wavelength; electron, alpha-particle, neutron and proton.
Answer: From De-Broglie relation relation for wavelength in terms of kinetic energy
![\[\lambda=\frac{h}{\sqrt{2m_0K}}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-e7f95df58425c811b10c47cb5b6be09e_l3.png "Rendered by QuickLaTeX.com")
We see that the particle which is heaviest, will have shortest wavelength. As mass of alpha-particle is greatest of all particles listed, so it will have shortest wavelength.
Q.5.4 why is the Heisenberg uncertainty principle not more apparent in our daily observations?
Answer: Uncertainty relation is,
∆p∆x ~ h/2π
Above equation shows why Heisenberg uncertainty principle is not more readily apparent in our daily observation. In classical limits, ‘h’ can be neglected and de-Broglie wavelength of ordinary objects is not detectable, so uncertainty principle is not apparent in daily observations.
Q.5.5 Does a photon have a de-Broglie wavelength? Explain.
Answer: In de-Broglie hypothesis an electromagnetic wave is the de-Broglie wave for a photon moving with speed ‘c’. The de-Broglie waves for electron, proton, neutron etc. are not electromagnetic waves but matter waves. The wavelength of proton according to de-Broglie hypothesis is,
![\[\lambda=\frac{h}{P}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-cb0f49edff4a5c88dd1bcc81c9fc6ec2_l3.png "Rendered by QuickLaTeX.com")
Where ‘p’ is momentum of photon.
Q.5.6 A beam of particles is diffracted from a crystal, producing an interference maximum at angle If mass of particle is increased, what happens to angle of interference maximum?
Answer: By increasing mass of particle, its de Broglie wavelength decreases, so from equation,
, angle of interference maximum decreases.
Q.5.7 Name at least two experiments which support the wave nature of matter.
Answer: Following two experiments support wave nature of matter:
- Davison and Germer experiment
- G. P. Thomson experiment
Q.5.8 Is an electron a particle? Is it a wave? Explain your answer, citing relevant experimental evidence.
Answer: We observe the wave property of electron in a diffraction experiment like Davison-Germer experiment, G.P. Thomson experiment etc. but not the particle. Also we observe the particle the particle property in J.J. Thomson’s measurement of for electron etc. but not the wave property. It is not possible to perform a single experiment in which electron will behave as a particle as well as wave.
Q.5.9 Name at least two experiments which support the particle nature of radiation.
Answer: Following two experiments support particle nature of radiation:
- Photoelectric effect
- Compton effect
Q.5.10 Is light a wave or a particle? Support your answer by citing specific experimental evidence.
Answer: Light has dual nature both wave and particle characteristics. In single and double slit experiments light behaves like a wave where as in the photoelectric effect and Compton Effect, light behaves like a particle. Light may be characterized as an electromagnetic wave with a particular wavelength or frequency, yet at the same time light may be characterized as a stream of photons, each carrying a discrete energy,
Q.5.11 Name at least one experiment in each case which supports the wave nature of matter and wave nature of radiation.
Answer: J.J. Thomson measurement of of electron supports wave nature of matter and Young double slit interference experiment supports wave nature of radiation.
Q.5.12 why an electron microscope is more suitable than an optical microscope for “seeing” objects less than 1 mm in size?
Answer: The wavelength of violet light is of order of whereas the de Broglie wavelength of an electron is smaller than this value. That is why an electron microscope is more suitable than an optical microscope.
Q.5.13 If an electron and proton have same de-Broglie wavelength, which particle has greater speed?
Answer: According to de-Broglie hypothesis, the wavelength associated with a particle is given by,
![\[\lambda=\frac{h}{mV}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow V=\frac{h}{m\lambda}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-1a109bda642f6cd6d72374efb975f73d_l3.png "Rendered by QuickLaTeX.com")
For same wavelength, the smaller mass has greater velocity. So electron will have greater speed.
Q.5.14 A proton has a slightly smaller mass than a neutron. Would a proton of same wavelength have more or less kinetic energy?
Answer: From de-Broglie relation for wavelength in terms of kinetic energy
![\[\lambda=\frac{h}{\sqrt{2m_0}K}\ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow\lambda^2=\frac{h^2}{2m_0K}\ \ \ \ \ \ \ \ \ \ \ \ \Rightarrow K=\frac{h^2}{2m_0\lambda^2}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-f17482abb4c9ccef9dcdd2c4dbfcaede_l3.png "Rendered by QuickLaTeX.com")
We see that for a given wavelength, kinetic energy is inversely proportional to the mass. Hence proton with smaller mass has more kinetic energy than neutron.
Q.5.15 Considering electron and photon as particles how are they different from each other?
Answer: Photon:
- A photon has no rest mass because it cannot be at rest w.r.t any observer.
- A photon moves with velocity of light.
- Momentum of a photon with frequency is P=hʋ/c
Electron:
- An electron has mass and may be at rest.
- An electron cannot move with velocity of light.
- Momentum of electron with mass ‘m’ moving with velocity v is P=mv
Q.5.16 The quantity 
, the amplitude of matter wave is called wave function. What is relation between this quantity and probability density? Why we give physical significance to probability and not to itself?
Answer: Relation between 
and probability density is that modulus square of gives probability density i.e.
![\[probabiltiy\ density=\ \left|\mathrm{\Psi}\left(x\right)\right|^2\ =\ \mathrm{\Psi}^\ast\ \left(x\right)\ \mathrm{\Psi}\ \left(x\right)\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-805cf712f552ef52a206cef86638c145_l3.png "Rendered by QuickLaTeX.com")
We give physical significance to 
instead of because is a complex quantity where as is a real quantity.
Q.5.17 why was the demonstration of electron diffraction by Davisson and Germer an important experiment?
Answer: The discovery of electron diffraction by Davisson and Germer was an important result concerning motion of material particles. The development of quantum mechanics made possible describing the motion of electrons in atoms; understanding molecular structure and the behavior of matter at the atomic scale, including electronics, photonics, and engineered materials; according for the motion of nucleons in nuclei; and studying elementary particles.
Q.5.18 If Plank’s constant were reduced to zero, would the uncertainties in position & momentum and energy and time be increased or decreased?
Answer: According to uncertainty principle,
∆Px∆x ~ћ
As h approaches to zero, uncertainties would decrease to zero.
Review Questions
R.5.1 If electrons behave only like particles, what pattern would you expect you expect on the screen after the electrons passes through the double slit?
Answer: If electrons behave only like particle, then there will no pattern on the screen like interference or diffraction after the electrons passes through the double slit.
R.5.2 what are advantages of an electron microscope over an optical microscope?
Answer: Resolving power of an electron microscope is thousand times greater than an optical microscope. Moreover magnification of electron microscope is far greater than an optical microscope.
R.5.3 If measurements show a precise position for an electron, can those measurements show precise momentum also?
Answer: If measurements show a precise position for an electron, by uncertainty principle momentum will not be precise.
R.5.4 When does light behave as wave? When dose it behave as particle?
Answer: When frequency of light is small as interference, diffraction and polarization of light then light behaves as wave. When frequency of light is large is large as photoelectric effect, Compton Effect, pair production and black body radiations then it behaves as particle.
R5.5 By what factor does the de-Broglie wavelength of a particle change if its momentum is doubled?
Answer: De-Broglie wavelength of a particle in terms of its momentum is given by,
![\[\lambda=\frac{h}{p}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-3318a590ea3d7f93e6c6d9146be2fe4e_l3.png "Rendered by QuickLaTeX.com")
From above relation it is clear that when momentum is doubled, then de-Broglie wavelength is halved.
R.5.6 By what factor does the de-Broglie wavelength of a particle change if its kinetic energy is doubled?
Answer: De-Broglie wavelength of a [article in terms of kinetic energy is given by,
From above relation it is clear that when kinetic energy is doubled, then de-Broglie wavelength increases by a factor of 
.
R.5.7 A beam of particles is diffracted from a crystal, producing an interference maximum at angle. If energy of particle is increased what happens to angle of interference maximum?
Answer: By increasing energy of particle, its de-Broglie wavelength decreases so from equation,
angle of interference maximum decreases.
R.5.8 what happens to uncertainty in x-component of momentum of a particle as
Answer: According to Uncertainty principle,
∆Px∆x ~ћ ⇒∆Px ~ ћ/∆x
When ∆x→0 then ∆Px →∞, that is momentum becomes uncertain.
