The ratio of the energy of a photon with $\lambda = 150\,nm$ to that with $\lambda = 300\,nm$ is

The energy flux of sunlight reaching the surface of the earth is $1.388 \times 10^{3} \; W/m^{2}$. How many photons (nearly) per square metre are incident on the Earth per second? Assume that the photons in the sunlight have an average wavelength of $550 \; nm$.

$A$ photon of wavelength $\lambda$ is scattered from an electron,which was at rest. The wavelength shift $\Delta \lambda$ is three times of $\lambda$ and the angle of scattering $\theta$ is $60^o$. The angle at which the electron recoiled is $\phi$. The value of $\tan \phi$ is: (electron speed is much smaller than the speed of light)

If the mean wavelength of light radiated by a $100 \ W$ lamp is $5000 \ \mathring{A}$,then the number of photons radiated per second is:

$A$ 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?

The minimum intensity of light that can be perceived by the human eye is $10^{-10} \ W/m^2$. If the area of the pupil is $10^{-6} \ m^2$ and the wavelength of light is $560 \ nm$,approximately how many photons per second enter the eye? (Use $h = 6.6 \times 10^{-34} \ J \cdot s$ and $c = 3 \times 10^8 \ m/s$).