Quiz4prep.pdf - Physics 7C Quiz 4 First Name Last Name ID...

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Physics 7C Quiz 4 First Name Last Name ID Section An electron (of mass m e = 9 . 11 × 10 31 kg) is placed in a one dimensional box with a side length of one angstrom (1 angstrom = 10 10 m, which is roughly the size of an atom). a). If the electron is in the ground state, what is its energy? The energy levels of a particle in a one-dimensional box is given by E n = h 2 n 2 8 mL 2 . For the ground state, recall n = 1, just as it would be for the fundamental of a 1D standing wave. Thus E 1 = h 2 8 mL 2 = (6 . 626 × 10 34 J · s) 2 8(9 . 11 × 10 31 kg)(1 × 10 10 m) 2 6 . 02 × 10 18 J (11) b). If the electron is in the ground state, what is its wavelength? What is the Sorry about the typo! Recall that the particle in a one-dimensional box has standing wave states that look like those of a string fi xed at both ends. Since for the ground state n = 1, we know that λ = 2 L 1 = 2 L = 2 × 10 10 m. (It was also possible to solve for the wavelength by using the fact that the energy found in part a was kinetic energy,
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