1195_Physics ProblemsTechnical Physics

1195_Physics ProblemsTechnical Physics - 536 Atomic Physics...

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536 Atomic Physics (b) 1.2 1 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 Probability Curve for Hydrogen r /a 0 FIG. P42.66 (c) The probability of finding the electron inside or outside the sphere of radius r is 1 2 . ∴+ + F H G I K J = 22 1 1 2 2 0 2 0 2 0 r a r a e ra or zz e z 2 ++= where z r a = 2 0 One can home in on a solution to this transcendental equation for r on a calculator, the result being = 134 0 . to three digits. P42.55 Let r represent the distance between the electron and the positron. The two move in a circle of radius r 2 around their center of mass with opposite velocities. The total angular momentum of the electron-positron system is quantized to according to L mvr mvr n n =+= = where n = 123 ,,, . For each particle, Fm a = expands to ke r mv r e 2 2 2 2 = . We can eliminate v n mr = = to find r mn mr e 2 2 = = . So the separation distances are r n mk e an n e == = ×
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