Physics 1 Problem Solutions 304

Physics 1 Problem Solutions 304 - true since the potential...

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300 Chapt. 40 More About Matter Waves where a = 0 . 529 ˚ A is the Bohr radius. The radial probability density (i.e., the probability density integrated over all solid angle times r 2 ) is ρ ( r ) = c | ψ | 2 r 2 d Ω = 4 r 2 a 3 e 2 r/a . The probability of Fnding the electron in a spherical shell of thickness dr is then dP = 4 r 2 a 3 e 2 r/a dr . a) What is the most probable radius r for Fnding the electron. b) Verify that the ground state wave function is normalized. HINT: You might Fnd the factorial integral useful: n ! = i 0 e x x n dx . c) Assume that our wave function is accurate right down to r = 0. (This can’t be exactly
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Unformatted text preview: true since the potential must change from a point charge form when one is very close to the proton or e±ectively inside of it.) What is the probability of Fnding the electron inside the nuclear region? Hydrogen, of course, has a boring one proton nucleus. We can take the outer radius of the nucleus to be a proton’s rms radius of r = 8 × 10 − 6 ˚ A. HINT: It seems perfectly reasonable to make a zeroth order expansion of the exponential factor in the probability density....
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This note was uploaded on 11/16/2011 for the course PHY 2053 taught by Professor Buchler during the Fall '06 term at University of Florida.

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