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quiz1_solution

# quiz1_solution - a 2 c s 2 =-2 a-c Solving the second two...

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Use dimensional analysis to estimate the binding energy of an electron on an atom. Energy has units of Joules (1J=1kg m 2 /s 2 ). The electron has mass m = 9.1 × 10 - 31 kg, charge e, ( e 2 = 2.3 × 10 - 28 Jm), and atoms obey quantum mechanics so the other possible variable is h = 1.05 × 10 -34 Js. Solution: E = ( e 2 ) a ( m ) b ( h ) c kg m 2 s 2 = kg m 3 s 2 a kg ( 29 b kg m 2 s C kg:1 = a + b + c m: 2 = 3
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Unformatted text preview: a + 2 c s: - 2 =-2 a-c Solving the second two equations gives a =2, c =-2, and the first then gives b =1. The final result is therefore E = C me 4 h 2 = C × 4.4 × 10-18 J where C is a numerical factor. C turns out to be 1/2 so dimensional analysis gives the correct answer to within a factor of 2....
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