Light of intensity $10^{-10} \ W/m^2$ and wavelength $5.6 \times 10^{-7} \ m$ is incident on a surface of area $10^{-6} \ m^2$. What is the number of photons incident per second?

$A$ 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?

$A$ 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]

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:

Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).

The photon energy in units of $eV$ for an electromagnetic wave of wavelength $2 \, cm$ is