Difficult Conceptual Numericals
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Dual Nature Of Radiation And Matter

A bulb lamp emits light of mean wavelength . The lamp is rated at and of the energy appears as emitted light. How many photons are emitted by the lamp per second?
Sun gives light at the rate of W of area perpendicular to the direction of light. Assume wavelength (sunlight) . Calculate the 
(a) Number of photons per second arriving at squared metres at earth.
(b) Number of photons emitted from the sun per second assuming that the average radius of earth's orbit is .
(a) How many photons of a radiation of wavelength must fall per second on a blackened plate inorder to produce a force of ?

(b) At what rate will the temperature of plate rise if it's mass is kg and specific heat equal to .
A plank of mass 'm' is lying on a rough surface having coefficient of friction in situation as shown in the figure. Find the acceleration of the plank assuming that it slips and surface of body exposed to radiation is black body.
The wavelength of light from the spectral emission line of sodium is . Find the kinetic energy at which (a) electron and (b) neutron would have the same De-Broglie wavelength. Given that mass of neutron .
Determine the De-Broglie wavelength of a proton, whose kinetic energy is equal to the rest mass energy of an electrons. Given that the mass of the electron is and mass of proton is times as that of the electron.
The stopping potential for photoelectrons emitted from a surface illuminated by a light wavelength of is . Calculate the maximum kinetic energy of photoelectrons, the work function of the surface, and the threshold frequency.
When a surface is irradiated with light of wavelength , a photocurrent appears which vanishes if a retarding potential greater than is applied across the phototude. When a different source of light is used, it is found that the critical retarding potential is changed to . Find the work function of the emitting surface and the wavelength of the second source. 
Find the frequency of light which ejects electron from a metal surface. Fully stopped by a retarding potential of , the photoelectric effect begins in this metal at a frequency of . Find the work function for this metal. 
Ultraviolet light of wavelengths and when allowed to fall on hydrogen atoms in their ground states is found to liberate electrons with kinetic energies and respectively. Find the value of Plank constant.