Particle (ideal gas) in thermal equilibrium with its surroundings has a kinetic energy of 3kT/2. Calculate the de Broglie wavelength for (a) a neutron at room temperature (300 K) and (b) a “cold” neutron at 77 K (liquid nitrogen).
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Particle (ideal gas) in thermal equilibrium with its surroundings has a kinetic energy of 3kT/2. Calculate the de Broglie wavelength for (a) a neutron at room temperature (300 K) and (b) a “cold” neutron at 77 K (liquid nitrogen).
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- 1.3. A photoelectric cell has a cutoff wavelength, λc, of 262.7 nm. ☹ (a) What is the work function of the cell? (b) What current would be produced by the cell if the wavelength was increased to 300 nm? 400 nm? 500 nm? (c) What stopping voltage Vo would be required if the illuminating wavelength were to be reduced to 200 nm? (d) What would be the maximum kinetic energy of the photo-electrons in the case of 200 nm illumination? ¹February 28, 2024 1An electron is in a box of width 3.0 * 10-10 m. What are the de Broglie wavelength and the magnitude of the momentum of the electron if it is in the n = 1 level.Light of wavelength 350 nm falls on a potassium surface, and the photoelectrons have amaximum kinetic energy of 1.3 eV.What is the work function of potassium?The speed of light is 3 × 108 m/s and Planck’sconstant is 6.63 × 10−34 J · s.Answer in units of eV. What is the threshold frequency for potassium?Answer in units of Hz.
- De Broglie postulated that the relationship ? = h/p is valid for relativistic particles. What is the de Broglie wavelength for a (relativistic) electron having a kinetic energy of 3.18 MeV?Calculate the de Broglie wavelength (in fm) of a 5.8 MeV a particle emitted from an atomic nucleus whose diameter is approximately 1.6 × 10¯14, fm Calculate its minimum kinetic energy (in keV) according to the uncertainty principle. keV Could this particle exist inside the nucleus? Yes No Explain. m.The smallest atoms can themselves exhibit quantum mechanical behavior Calculate the de Broglie wavelength (in picometers) of a hydrogen atom traveling at 430 m/sm/s. Express your answer using three significant figures.
- The nucleus of an atom is on the order of 10-14 m in diameter. For an electron to be confined to a nucleus, its de Broglie wavelength would have to be on this order of magnitude or smaller. What would be the kinetic energy of an electron confined to this region?A) Astronomers measure the peak wavelength of a nearby star to be 410 nm. What is the star's temperature? B) How much energy does a single photon of light have at this wavelength? C) An electron bound in an unknown metal requires 1.45E-19 ] of energy under the photoelectric effect to become free of the metal. How much kinetic energy would it have if struck by the photon froft part (b)? D) What is the final speed of the elctron from part (c)?In an electron microscope, we wish to study particles of a diameter of about 0.10μm (about 1000 times the size of a single atom). What should be the de Broglie wavelength of the electrons?