Calculate the de Broglie wavelength of (a) an oxygen (O2) molecule darting around the room at 480 m/s and (b) an Escherichia coli bacterium of mass 6.5x10-13 kg, which has been measured to move at a speed of 1.0 x 10-5 m/s.
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Calculate the de Broglie wavelength of (a) an oxygen (O2) molecule darting around the room at 480 m/s and (b) an Escherichia coli bacterium of mass 6.5x10-13 kg, which has been measured to move at a speed of 1.0 x 10-5 m/s.
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- Calculate the velocities of electrons with de Broglie wavelengths of 1.7×103 nm and 5.0 nm, respectively.An electron is moving with a speed of 3.00 x 10° m/s. What is the speed of a proton that has the same de Broglie wavelength as this electron? O 1.63 km/s O 2.18 km/s O 163 m/s 1.63 m/s O 1.36 km/sCalculate 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/s
- A 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?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?