An electron is in a box of width 3.0x10-10 m. What are the de Broglie wavelength and the magnitude of the momentum of the electron if it is in the n = 3 level.
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An electron is in a box of width 3.0x10-10 m. What are the de Broglie wavelength and the magnitude of the momentum of the electron if it is in the n = 3 level.
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- Calculate the de Broglie wavelength of a proton moving at 2.60 x 104 m/s and 1.99 x 108 m/s. (a) 2.60 x 104 m/s m (b) 1.99 x 108 m/sA free electron moving along the x-direction (one for which V(x) = 0) would have a wave function of the form f(x) = A eikx + B e−ikx where A and B are constants. (a) If the wavelength of this wave function (in radians) equals the de Broglie wavelength of the electron, and its velocity, v = 8.40 × 10² m/sec, what is the value of k (in nm¯¹)? Express your answer in scientific notation with three significant figures. (b) The Hamiltonian operator for a free electron is given by p² ħ² d² Ĥ 2me 2me dx² The wave function provided at the top is an eigenstate of Â. If one measures the energy for an electron in this state using Â, what would be the result, and how does it compare to the classical kinetic energy of a free electron with this velocity?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?
- Light of wavelength 340 nm, 600 nm and 680 nm is incident on a metal. Electrons are not emitted from the metal, which of the following is the most likely scenario. The energy of the photon for 600 nm light corresponds to the work function of the material. The energy of the photon for 680 nm light corresponds to the work function of the material. The work function is less than any of these photon energies. The work function is more than any of these photon energies. The energy of the photon for 340 nm light corresponds to the work function of the material.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?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?