1. (a)What voltage should be applied to accelerate an electron from zero velocity in order that it acquire the same energy as a photon of wavelength λ.-087 μm? (b) A photon of wavelength 1.06 μmis combined with a photon of wavelength 10.6 yum to create a photon whose energy is the sum of the energies of the two photons. What is the wavelength of the resultant photon? 2. Compare the total momentum of the photons in a 10-J laser pulse with that of a 1-g mass moving at a velocity of 1 cm/s and with an electron moving at a velocity co/ 10. 3. Assume that a 100-pW He-Ne single-mode laser emits light at 633 nm in a TEMao Gaussian beam. (a) What is the mean number of photons crossing a circle of radius equal to the waist radius of the beam Wo in a time T = 100 ns? (b) What is the root-mean-square value of the number of photon counts in (a)? (c) What is the probability that no photons are counted in (a)? 4. Consider an isolated hydrogen atom of mass 1.66 x 1027 kg. (a) Find the gravitational force on this hydrogen atom near the surface of the earth (assume that at sea level the gravitational acceleration constant g= 9.8 m/s) (b) Let an upwardly directed laser beam emitting 1-eV photons be forced in such a way that the full momentum of each of its photons is transferred to the atom. Find the average upward force on the atom provided by one photon striking each second. (c) Find the number of photons that must strike the atom per second, and the (d) How many photons per second would be required to keep the atom from falling Show that the power of a monochromatic optical beam that carries an average of one corresponding optical power, for it not to fall under the effect of gravity, given idealized conditions in vacuum. if it were perfectly reflecting? 5. photon per optical cycle is inversely proportional to the squared wavelength.
