$A$ photon falls through a height of $1 \, km$ in the earth's gravitational field. To calculate the change in its frequency,take its mass to be $h \nu / c^{2}$. The fractional change in frequency $\nu$ is close to

An electron and a proton are detected in a cosmic ray experiment,the first with kinetic energy $10 \; keV$,and the second with $100 \; keV$. Which is faster,the electron or the proton? Obtain the ratio of their speeds. (Electron mass $= 9.11 \times 10^{-31} \; kg$,proton mass $= 1.67 \times 10^{-27} \; kg$,$1 \; eV = 1.60 \times 10^{-19} \; J$)

Two monochromatic beams $A$ and $B$ of equal intensity $I$ hit a screen. The number of photons hitting the screen by beam $A$ is twice that by beam $B$. What inference can you make about their frequencies?

Consider the figure for photoemission. How would you reconcile this with the law of conservation of momentum? Note that light (photons) has 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 < target area).
$(c)$ How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

Solar energy is incident normally on the earth's surface at the rate of about $1.4 \, kW m^{-2}$. The distance between the earth and the sun is $1.5 \times 10^{11} \, m$. Energy $E$ and mass $m$ are related by Einstein's equation $E = mc^2$,where $c = 3 \times 10^8 \, m s^{-1}$ is the speed of light in free space. The decrease in the mass of the sun is ........... $\, kg s^{-1}$.