Consider a beam of electrons (each electron with energy \({ E }_{ 0 }\)) incident on metal surface kept in an evacuated chamber. Then

An electron is moving with an initial velocity \(\frac { h }{ mv } ={ v }_{ 0 }\overset { \wedge }{ L } \) and is in a magnetic field \(\vec { B= } \ { B }_{ 0 }\vec { j } \) Then its de-Broglie wavelength

Photons absorbed in matter are converted to heat.A source emitting n photon/sec frequency v is used to convert 1 kg of ice at \({ 0 }^{ 0 }c \) . Then the time t taken for the conversation.

The maximum velocity of an electron emitted by light of wavelength \(\lambda \)incident on the surface of a metal of wor4k function \(\phi \) is[h = Plank's constant, c = speed of light and m = mass of electron]

What is the effect of a decrease in frequency of incident radiation on the stopping potential in photoelectric emission?

The photoelectric current at a distance \({ r }_{ 1 }and{ r }_{ 2 }\)of light source from the photoelectric cell is respectively\({ I }_{ 1 }and{ I }_{ 2 }\). Find the value of.\({ I }_{ 1 }/{ I }_{ 2 }\)

The de-Broglie Wavelength of a particle of kinetic energy K is \({ \lambda }\) What would be the de-Broglie wavelength of the particle, if its kinetic energy were K/4? 

In Davisson-Germer experiment, if the angle of diffraction is then\(52°,\) find the glancing angle.

de-Broglie wavelength associated with an electron accelerated through a potential difference V is \({ \lambda }.\) What will be its wavelength when the accelerating potential is increased to 4V?

For a photosensitive surface, threshold wavelength is.\({ \lambda }_{ 0 }\) Does photoemission occur if the wavelength of the incident radiation is (i) more than \({ \lambda }_{ 0 }\) (ii) less than\({ \lambda }_{ 0 }\) Justify your answer?

If we go on increasing the wavelength of light incident on a metal surface, what changes in the number of electrons and the energy take place?

Write two characteristic features observed in photoelectric effect which support the photon picture of electromagnetic radiation.

Consider figure for photoemission. How would you reconcile with momentum conservation? Note light (photons) have momentum in a different direction than the emitted electrons.

Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW.
(a) Find the energy and momentum of each photon in the light beam.
(b) How many photons per second on the average arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area) and
(c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

(a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 x 10^-10m?
(b) Also find the de Broglie wavelength of a neutron in thermal equilibrium with matter having an average kinetic energy of 3/2 kT at 300K.

An Electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure (\(-{ 10 }^{ 2 }\) mm of Hg).A magnetic field of 2.83 x 10^-4 T curves the path of the electrons in a circular orbit of radius 12.0 cm. Determine e/m from the data.

Answer the following question.
(a) Quarks inside protons and neutrons are thought to carry fractional charges \(\left( +\frac { 2 }{ 3 } e,-\frac { 1 }{ 3 } e \right) .\) Why do they not show up in Millikan's oil drop experiment?
(b) What is so special about the combination elm? Why do we not simply talk of e and \(m\) specially?
(c) Why should gases be insulators at ordinary pressure and start conducting at very low pressure.
(d) Every metal has a definite work function, Why do photoelectrons not come out all with same energy if incident radiations is monochromatic?Why is there an energy distribution of photoelectrons?
(e) The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations : \(E=hv,p=\frac { h }{ \lambda } \)
But while the value of  \(\lambda \) is physically significant, the value of \(v\) (and therefore the value of the phase speed \(v\lambda \)) has no physical significance. Why?

Radiation has dual nature,i.e., it possesses the properties of both; wave and particle.This prompted de-Broglie to predict dual nature of moving material particles.Thus waves are associated with moving material particles which are called matter waves. The wavelength of matter wave is given by \(\lambda =\frac { h }{ mv } \), where m is the mass, v is the speed of the particle and h is Plank's constant. Read the above paragraph and answer the following questions;
(i) How was the wave nature of the electron established?
(ii) What are the de-Broglie wavelength associated with a particle (i) at rest (ii) moving with infinite speed?
(iii) What are the basic values displayed with this study?

The main aim of Davisson and Germer was to study about nickel surface by directing beam of electrons at its surface and note the number of electrons that bounced off at different angles. The carried out their experiment inside a vacuum chamber where an air after entering the chamber gives an oxide film on nickel  surface. Again the does their experiment and found that the electrons which hits  the nickel surface were scattered by atoms that appears from crystal planes in  nickel crystal. By doing their regular experiment, Davisson and Germer's at once found diffraction of electrons which was an initial proof that confirm about de Broglie's hypothesis and shows wave properties in particles.
(a) What can we infer about the values shown by Davisson and Germer?
(b) Write the expression to find the wavelength of an electron when accelerated through a potential difference of V volts.

The extent of localisation of a particle is determined by its de-Broglie wavelength.If an electron is localised within the nucleus(of size about \({ 10 }^{ -14 }\))of an atom, what is it energy? Compare this energy with the typical binding energies(of the order of a few MeV) in a nucleus and hence argue why electron cannot reside in a nucleus.