An 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 = 2 level.
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Q: An electron is in a box of width 3.0 * 10-10 m. What are the de Broglie wavelength and the magnitude…
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An 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 = 2 level.
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- A nonrelativistic particle of mass m and charge q is accelerated from rest through a potential difference Δ V (a) Use conservation of energy to find a symbolic expression for the momentum of the particle in terms of m , q, and ΔV (b) Write a symbolic expression for the de Broglie wavelength using the result of part (a). (c) If an electron and proton go through the same potential difference but in opposite directions, which particle will have the shorter wavelength?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?By what factor does the de Broglie wavelength of a particle change if (a) its momentum is doubled or (b) its kinetic energy is doubled?
- A) After a 0.790 nm x-ray photon scatters from a free electron, the electron recoils with a speed equal to 1.59E+6 m/s. What was the Compton shift in the photon's wavelength? B) Through what angle was the photon scattered?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?Light with wavelength ? = 635 nm is incident on a metallic surface. Electrons are ejected from the surface. The maximum speed of these electrons is v = 4.40 ✕ 105 m/s. a) What is the work function of the metal (in eV)? b) What is the cutoff frequency for this metal (in Hz)?
- a) Find the de Broglie wavelength of electrons moving with an average speed of 1.55 x 105 m/s. b) Suppose these electrons are described by a wave packet of width 2.55 nm. What is the uncertainty of the momentum of the electrons?A photon with wavelength 0.1100 nm collides with a free electron that is initially at rest. After the collision the wavelength is 0.1132 nm. (a) What is the kinetic energy of the electron after the collision? What is its speed? (b) If the electron is suddenly stopped (for example, in a solid target), all of its kinetic energy is used to create a photon. What is the wavelength of this photon?