Exam 37: Photons: Light Waves Behaving As Particles

A nonrelativistic electron is confined to a length of 500 pm on the x-axis. What is the kinetic energy of the electron if its speed is equal to the minimum uncertainty possible in its speed? ( = 1.055 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

If the accuracy in measuring the velocity of a particle increases, the accuracy in measuring its position will

A certain particle's energy is measured by a detector to within 1.0 × 10^-18. What is the minimum uncertainty we can have in its arrival time at the detector? ( = 1.055 × 10^-34 J ∙ s)

When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J, mel = 9.11 × 10^-31 kg) (a) What is the work function of the metal, in eV? (b) What is the maximum speed of the ejected electrons?

In a photoelectric effect experiment, electrons emerge from a copper surface with a maximum kinetic energy of 1.10 eV when light shines on the surface. The work function of copper is 4.65 eV. Which one of the following values is closest to the wavelength of the light? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV. What is the threshold frequency for photoelectron production? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A small dust particle of mass 7.90 × 10^-6 g is being observed under a magnifying lens. Its position is determined to within 0.0050 mm. (1 y = 3.156 × 10⁷ s, = 1.055 × 10^-34 J ∙ s) (a) Find the minimum uncertainty in its velocity implied by the uncertainty in its position. (b) Assuming the dust particle is moving at the speed you just found, how many years would it take for the particle to move 1.0 mm?

The energy of an electron state has an uncertainty of 0.500 eV. What is the minimum uncertainty in the lifetime of the level? ( = 1.055 × 10^-34 J ∙ s = 6.591 × 10^-16 eV ∙ s, 1 eV = 1.60 × 10^-19 J)

A stopping potential of 0.50 V is required when a phototube is illuminated with monochromatic light of wavelength 590 nm. Monochromatic light of a different wavelength is now shown on the tube, and the stopping potential is measured to be 2.30 V. What is the wavelength of this new light? (c = 3.00 × 10⁸ m/s, e = - 1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A metal having a work function of 2.5 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. For which one of the following ranges of the wavelength band in this white light are photoelectrons NOT produced? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A photon of initial wavelength 0.651 nm, after being scattered from a free electron at rest, moves off at an angle of 120° with respect to its incident direction. (mel = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s) (a) What is the wavelength of the scattered photon? (b) What is the energy of the scattered photon?

Upon being struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of 1.45 eV. What is the work function of this metal? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A beam of red light and a beam of violet light each deliver the same power on a surface. For which beam is the number of photons hitting the surface per second the greatest?

Light of wavelength 400 nm falls on a metal surface having a work function 1.70 eV. What is the maximum kinetic energy of the photoelectrons emitted from the metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s = 4.141 × 10^-15 ev ∙ s, 1 eV = 1.60 × 10^-19 J)

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy 4.1 × 10^-13 J? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A photon of wavelength 18.0 pm is scattered through an angle of 120° by a stationary electron. What is the wavelength of the scattered photon? (mel = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

An ultraviolet source produces a monochromatic beam of 200-nm light. A shutter allows a pulse to pass that is 10,000 wavelengths long. The uncertainty in the energy of a photon in this pulse is closest to which of the following? ( = 1.055 × 10^-34 J ∙ s = 6.59 × 10^-16 eV ∙ s, c = 3.00 × 10⁸ m/s)

Monochromatic light strikes a metal surface and electrons are ejected from the metal. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons?