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 ........... $\, kg s^{-1}$.

$A$ laser produces a beam of light of frequency $5 \times 10^{14} \,Hz$ with an output power of $33 \,mW$. The average number of photons emitted by the laser per second is (Planck's constant $h = 6.6 \times 10^{-34} \,J \,s$)

What is the velocity of a photon?

$A$ scientist claims to have a perfect technique in which he can spontaneously convert an electron completely into energy in the laboratory without any other material required. What is the conclusion about this claim from our current understanding of physics?

Monochromatic light of frequency $6 \times 10^{14} \text{ Hz}$ is produced by a laser. The power emitted is $4 \times 10^{-3} \text{ W}$. How many photons per second on an average are emitted by the source? $[h = 6.63 \times 10^{-34} \text{ Js}]$

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?