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# ps8 - Physics 212 Problem Set 8 Spring 2010 1 Show that the...

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Physics 212 – Problem Set 8 – Spring 2010 1. Show that the relationship we obtained from imposing the condition that our atoms are in a steady state of thermal equilibrium at temperature T and the applied radiation field is also in thermal equilibrium at temperature T : B ij ¯ 3 π 2 c 3 1 e ¯ hω/kT - 1 A ji + B ji ¯ 3 π 2 c 3 1 e ¯ hω/kT - 1 = g j g i e - ¯ hω/kT requires that g i B ij = g j B ji and A ji = ¯ 3 π 2 c 3 B ji if the Einstein coefficients are independent of temperature. 2. Show that the number of photon states per unit volume per unit frequency range for radiation confined to a box is ω 2 π 2 c 3 . 3. Obtain the lifetime of the n = 2, l = 1 level of hydrogen against spontaneous decay by dipole radiation. 4. Show (I already sketched this in class; you need to justify the steps) that the ratio of the typical size of a magnetic dipole matrix element to the typical size of an electric dipole matrix element is , for a hydrogenic atom with Z protons. Find the ratio of a typical quadrupole matrix element to a typical electric dipole matrix

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ps8 - Physics 212 Problem Set 8 Spring 2010 1 Show that the...

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