Monochromatic light of wavelength $3000\, \mathring A $ is incident on a surface area $4\ cm^2$. If intensity of light is $150\, mW/m^2$, then rate at which photons strike the target is

Estimating the following two numbers should be interesting. The first number will tell you why radio engineers do not need to worry much about photons! The second number tells you why our eye can never ‘count photons’, even in barely detectable light.

$(a)$ The number of photons emitted per second by a Medium wave transmitter of $10\; kW$ power, emitting radiowaves of wavelength $500\; m$.

$(b)$ The number of photons entering the pupil of our eye per second corresponding to the minimum intensity of white light that we humans can percetve $(-10^{-10}\; W m ^{-2}$). Take the area of the pupil to be about $0.4 \;cm ^{2}$, and the average frequency of white light to be about $6 \times 10^{14}\; Hz$

The momentum of a photon with energy $20\, eV$ is

A $100 \;W$ sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is $589\; nm$.

$(a)$ What is the energy per photon associated with the sodium light?

$(b)$ At what rate are the photons delivered to the sphere?

A small object at rest, absorbs a light pulse of power $20\,mW$ and duration $300\,ns$. Assuming speed of light as $3 \times 10^8\,m / s$. the momentum of the object becomes equal to $.........\times 10^{-17} kg\,m / s$

A 1$\mu$ $A$ beam of protons with a cross-sectional area of $0.5$ sq. mm is moving with a velocity of $3 \times {10^4}m{s^{ - 1}}$. Then charge density of beam is