The potential energy U is zero within the potential well (in the interval 0 . x . L) and has the constant value U, outside this interval. U(x) U.
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An electron is moving past the square well shown in Fig. . The electron has energy E = 3U0 . What is the ratio of the de Broglie wavelength of the electron in the region x 7 L to the wavelength for 0 6 x 6 L?
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- An electron is accelerated through a potential difference ΔV. A second electron is accelerated through a potential difference that is twice as large. Which electron has a shorter de Broglie wavelength?Light of frequency 12x1015 Hz shines on to clean caesium metal. What is the maximum kinetic energy of the electrons emitted ? The work function of caesium is 1.5 x 10-19 J and the Planck constant h = 6.63 x 10-34 J s. Round off the answer to 2 decimal places and write answers as power of 10.In a photoelectric experiment it is found that a stopping potential of 1.00 V is needed to stop all the electrons when incident light of wavelength 264 nm is used and 2.3 V is needed for light of wavelength 207 nm. From these data determine Planck's constant. (Enter your answer, in eV · s, to at least four significant figures.) eV s From these data determine the work function (in eV) of the metal. eV
- The wavelength of a red spectral emission line is 670.0 nm. At what kinetic energy (in J) would an electron have that wavelength as its de Broglie wavelength?Electrons with an energy of 0.842 eV are incident on a double slit in which the two slits are separated by 40.0 nm. What is the de Broglie wavelength (in nanometers!) of these electrons?An electron is accelerated from rest through a potential difference of 100 V. What is the de Broglie wavelength of the electron?
- The velocity of an electron is known to be 1.000×105 m/s, with an uncertainty of Av = 1.00×102 m/s. (a) What is the minimum uncertainty in the electron's position, Av, in meters? (b) How does this compare to the de Broglie wavelength of the electron? (c) One of your professors (m = 75.0 kg) is pacing at the front of the classroom, and you measure their velocity to an uncertainty of Av = 0.100 m/s. What is the minimum uncertainty in a measurement of their position? (d) How does this compare to the height of your professor?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 ball has a mass of 0.0972 kg just before itstrikes the Earth after being dropped from abuilding 22.5 m tall.What is its de Broglie wavelength? The acceleration of gravity is 9.8 m/s2and Planck’sconstant is 6.62607 × 10−34 J · s.Answer in units of m.