Calculate the number of photons entering the eye of a duck per second,corresponding to the minimum intensity of white light $(\sim 10^{-10} \ W/m^2)$. Take the area of the duck's eye as $0.4 \ cm^2$ and the average frequency of white light as $6 \times 10^{14} \ Hz$.

$A$ perfectly reflecting mirror of mass $M$ mounted on a spring constitutes a spring-mass system of angular frequency $\Omega$ such that $\frac{4 \pi M \Omega}{h} = 10^{24} \text{ m}^{-2}$,where $h$ is Planck's constant. $N$ photons of wavelength $\lambda = 8 \pi \times 10^{-6} \text{ m}$ strike the mirror simultaneously at normal incidence such that the mirror gets displaced by $1 \mu\text{m}$. If the value of $N$ is $x \times 10^{12}$,then the value of $x$ is. . . . . . . . [Consider the spring as massless]

$A$ particle which has zero rest mass and non-zero energy and momentum must travel with a speed

The momentum of a photon of energy $1 \text{ MeV}$ in $\text{kg-m/s}$ will be

Find the number of photons emitted per second by a $10 \ kW$ radio transmitter operating at a wavelength of $500 \ m$.

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 $= 1.67 \times 10^{-27} \; kg$,$1 \; eV = 1.60 \times 10^{-19} \; J$)