The wavelength of a photon with energy $35 \text{ keV}$ is . . . . . . .
$(h = 6.625 \times 10^{-34} \text{ J s}, c = 3 \times 10^{8} \text{ m/s}, 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J})$

There are materials which absorb photons of shorter wavelength and emit photons of longer wavelength. Can there be stable substances which absorb photons of larger wavelength and emit light of shorter wavelength?

If $h$ is Planck's constant in $SI$ system,the momentum of a photon of wavelength $0.01 \, \mathring{A}$ is:

$10^{20}$ photons of wavelength $660 \ nm$ are emitted per second from a lamp. The wattage of the lamp is (Planck's constant $h = 6.6 \times 10^{-34} \ J \cdot s$). (in $W$)

$(a)$ When monochromatic light is incident on a surface separating two media,the reflected and refracted light both have the same frequency as the incident frequency. Explain why?
$(b)$ When light travels from a rarer to a denser medium,the speed decreases. Does the reduction in speed imply a reduction in the energy carried by the light wave?
$(c)$ In the wave picture of light,intensity of light is determined by the square of the amplitude of the wave. What determines the intensity of light in the photon picture of light?

$A$ $200\, W$ sodium street lamp emits yellow light of wavelength $0.6\, \mu m$. Assuming it to be $25\%$ efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is: