Dual Nature of Radiation and Matter

Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.

The work function of caesium metal is 2.14 eV. When light of frequency $6 \times$10^{14}$$ Hz is incident on the metal surface, photoemission of electrons occurs. What is the (a) maximum kinetic energy of the emitted electrons, (b) Stopping potential, and (c) maximum speed of the emitted photoelectrons?

The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted?

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 less than the target area), and (c) How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

In an experiment on photoelectric effect, the slope of the cut-off voltage versus frequency of incident light is found to be $4.12 \times$10^{-15}$$ Vs. Calculate the value of Planck's constant.

The threshold frequency for a certain metal is $3.3 \times$10^{14} Hz. If light of frequency $8.2 \times$10^{14}$$ Hz is incident on the metal, predict the cut-off voltage for the photoelectric emission.

The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?

Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.

What is the de Broglie wavelength of (a) a bullet of mass 0.040 kg travelling at the speed of 1.0 km/s, (b) a ball of mass 0.060 kg moving at a speed of 1.0 m/s, and (c) a dust particle of mass $1.0 \times$10^{-9}$$ kg drifting with a speed of 2.2 m/s?

Show that the wavelength of electromagnetic radiation is equal to the de Broglie wavelength of its quantum (photon).