p40_055 - p = µ 4 r 2 ∆ r a 3 ¶ e − 2 r/a = 4(0 ....

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55. Since ∆ r is small, we may calculate the probability using p = P ( r )∆ r ,where P ( r ) is the radial proba- bility density. The radial probability density for the ground state of hydrogen is given by Eq. 40-31: P ( r )= µ 4 r 2 a 3 e 2 r/a where a is the Bohr radius. (a) Here, r =0 . 500 a and ∆ r =0 . 010 a . Then,
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Unformatted text preview: p = µ 4 r 2 ∆ r a 3 ¶ e − 2 r/a = 4(0 . 500) 2 (0 . 010) e − 1 = 3 . 68 × 10 − 3 . (b) We set r = 1 . 00 a and ∆ r = 0 . 010 a . Then, p = µ 4 r 2 ∆ r a 3 ¶ e − 2 r/a = 4(1 . 00) 2 (0 . 010) e − 2 = 5 . 41 × 10 − 3 ....
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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