Specific heat of water is $4.2 \, J/g^{\circ}C$. If light of frequency $3 \times 10^9 \, Hz$ is used to heat $400 \, g$ of water from $20^{\circ}C$ to $40^{\circ}C$,the number of photons needed will be:

The energy of a photon of light of wavelength $450 \ nm$ is

The radiant energy from the Sun incident on the Earth's surface is $2 \ cal/cm^2 \cdot min$. If the average wavelength of solar radiation is $5500 \ \mathring A$,then the number of photons incident per minute on a surface area of $1 \ cm^2$ on the Earth's surface is ............ $(h = 6.6 \times 10^{-34} \ J \cdot s, 1 \ cal = 4.2 \ J)$

$A$ lamp of power $942 \ W$ radiates energy uniformly in all directions. The wavelength of radiation is $660 \ nm$. The photon flux on a small screen $5.0 \ m$ from the lamp in units of $\frac{\text{photon}}{m^2 \cdot s}$ is (Take Planck's constant $h = 6.6 \times 10^{-34} \ J \cdot s$ and speed of light $c = 3 \times 10^8 \ m/s$)

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

The wavelength of an electron and a photon are equal. If the energy of the photon is $E$ and the momentum of the electron is $p$,what is the value of $p/E$?