An electron has a de Broglie wavelength of 2.00 pm. Find its kinetic energy and the phase and group velocities of its de-Broglie waves.
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An electron has a de Broglie wavelength of 2.00 pm. Find its kinetic energy and the phase and group velocities of its de-Broglie waves.
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- ASK YOUR (a) What is the de Broglie wavelength (in m) of an electron moving at a speed of 3.03 x 104 m/s? (b) What is the de Broglie wavelength (in m) of an electron moving at a speed of 2.01 x 10° m/s? Need Help? Read ItCalculate the velocities of electrons with de Broglie wavelengths of 1.7×103 nm and 5.0 nm, respectively.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 = 1 level.
- 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?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?