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3063_Exam2_sp06

# 3063_Exam2_sp06 - PHY3063 Spring 2006 R D Field PHY 3063...

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PHY3063 Spring 2006 R. D. Field Exam 2 Page 1 of 8 March 9, 2006 PHY 3063 Exam 2 Name_____________________ Problem 1 (25 points): Consider an “atom” consisting of a proton and a muon. A proton has an electric charge +e and rest mass energy M p c 2 940 MeV. A muon is an elementary particle with charge –e similar to an electron but with a mass that is 207 times the mass of an electron (m e c 2 0.511 MeV). Use Bohr’s model of an atom to calculate the following: (a) (8 points) The radius of the first Bohr orbit ( i.e. the ground state) of the muonic “atom” ( in fm ). (b) (8 points) The ground state energy of the muonic “atom” ( in keV ). (c) (9 points) The ground state energy of the hydrogen atom can be estimated using the uncertainty relation. For a hydrogen atom in the ground state the uncertainty r in the position of the electron is approximately the 1 st Bohr radius, r 0 , consequently the electron’s momentum p r is uncertain by about r / h . Compute the ground state energy of the hydrogen atom ( in eV ), r Ke m p E e r 2 2 2 = , by setting r = r 0 and 0 / r p p r r h = = , where r 0 is the Bohr radius of the ground state.

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PHY3063 Spring 2006 R. D. Field Exam 2 Page 2 of 8 March 9, 2006 PHY 3063 Exam 2 Name_________________
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3063_Exam2_sp06 - PHY3063 Spring 2006 R D Field PHY 3063...

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