quiz3-su - r of the electron’s orbit(d What do you think...

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Physics 2D Quiz #3 Department of Physics, UCSD Summer Session II - 2009 Prof. Pathria 21 August 2009 Some Useful Data Speed of light: c = 2 . 998 × 10 8 m/s. Planck’s constant: h = 6 . 626 × 10 - 34 J · s Coulomb constant: k = 8 . 99 × 10 9 Nm 2 /C 2 Rydberg constant: R = 1 . 097 × 10 7 m - 1 Electron charge: e = 1 . 602 × 10 - 19 C 1 eV = 1.602 × 10 - 19 J Electron rest mass: m e = 9 . 11 × 10 - 31 kg Electron rest mass energy: m e c 2 = 0 . 511 MeV Energy of H atom in ground state: E 1 = - 13 . 6 eV Bohr radius: a 0 = 0 . 0529 nm de Broglie wavelength: λ = h/p p = 1 c p E 2 - ( m 0 c 2 ) 2 = 1 c 2 m 0 c 2 K + K 2 Uncertainty relations: Δ x Δ p h/ 4 π Δ E Δ t h/ 4 π Instructions Please write your answers in your blue book, and make sure your secret code number is written on all pages in indelible ink. 1
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1. A hydrogen atom happens to be in a state in which its total energy E (kinetic plus potential) is -3.4 eV. (a) Using this information, or otherwise, determine the kinetic energy K and the potential energy U of the system. (b) Using the value of K found above, determine the wavelength λ of the electron. (c) Next, using the value of U , determine the radius
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Unformatted text preview: r of the electron’s orbit. (d) What do you think should be the relationship between r and λ in the given state of the atom? Check if your values of r and λ satisfy this relationship. 2. Calculate the frequency f of the photon emitted by a hydrogen atom making a transition from the state n = 4 to the state n = 3. Compare your result with the frequency of revolution f * of the electron in these two orbits. 3. Through what potential difference would an electron have to be accelerated so that it has a de Broglie wavelength of: (i) 0.18 nm? (ii) 0.0018 nm? 4. Consider a photon and an electron that have a common wavelength λ , while the energy E γ of the photon is one-half of the total energy E e of the electron. (a) What is the value of λ in nm? (b) What are the values of E γ and E e in Mev? (c) What is the speed of the electron in m/s? 2...
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quiz3-su - r of the electron’s orbit(d What do you think...

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