In an accelerator experiment on high-energy collisions of electrons with positrons,a certain event is interpreted as annihilation of an electron-positron pair of total energy $10.2 \; BeV$ into two $\gamma$-rays of equal energy. What is the wavelength associated with each $\gamma$-ray? $(1 \; BeV = 10^9 \; eV)$

If $E$ and $P$ are the energy and the momentum of a photon respectively,then on reducing the wavelength of the photon:

The momentum of a photon is $2 \times 10^{-16} \text{ g} \cdot \text{cm/s}$. Its energy is:

$A$ laser produces a beam of light of frequency $5 \times 10^{14} \,Hz$ with an output power of $33 \,mW$. The average number of photons emitted by the laser per second is (Planck's constant $h = 6.6 \times 10^{-34} \,J \,s$)

$A$ 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?

Monochromatic light of wavelength $632.8 \; nm$ is produced by a helium-neon laser. The power emitted is $9.42 \; mW$.
$(a)$ Find the energy and momentum of each photon in the light beam.
$(b)$ How many photons per second,on the average,arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is < target area).
$(c)$ How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?