# hw5 - 4 4-1 4(a rn = n 2 h2 where n = 1 2 3 K me ke 2 rn =...

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4 4-14 (a) r n = n 2 h 2 m e ke 2 ; where n = 1, 2, 3, K r n = n 2 1.055 " 10 # 34 Js ( ) 2 9.11 " 10 # 31 kg ( ) 9.0 " 19 9 Nm 2 2 ( ) 1.6 " 10 # 19 C ( ) 2 = 0.052 9 nm ( ) n 2 For n = 1: r n = 0.052 9 nm For n = 2: r n = 0.2121 nm For n = 3: r n = 0.477 2 nm (b) From Equation 4.26, v = ke 2 m e r " # \$ % & 1 2 v 1 = 8.99 " 10 9 Nm 2 2 ( ) 1.60 " 10 # 19 C ( ) 2 9.11 " 10 # 31 kg ( ) 0.052 9 " 10 # 9 m ( ) \$ % & & & ( ) ) ) = 2.19 " 10 6 v 2 = 1.09 " 10 6 v 3 = 7.28 " 10 5 (c) As c = 3.0 " 10 8 , v << c and no relativistic correction is necessary. 4-17 r = n 2 h 2 Zm e ke 2 = n 2 Z " # \$ % & h 2 m e ke 2 " # \$ % & ; n = 1 r = 1 Z 1.055 " 10 # 34 Js ( ) 2 9.11 " 10 # 31 kg ( ) 9 " 10 9 Nm 2 C 2 ( ) 1.6 " 10 # 19 C ( ) 2 \$ % & & & ( ) ) ) = 5.30 " 10 # 11 m Z (a) For He + , Z = 2 , r = 5.30 " 10 # 11 m 2 = 2.65 " 10 # 11 m = 0.026 5 nm (b) For Li 2 + , Z = 3 , r = 5.30 " 10 # 11 m 3 = 1.77 " 10 # 11 m = 0.017 7 nm (c) For Be 3 + , Z = 4 , r = 5.30 " 10 # 11 m 4 = 1.32 " 10 # 11 m = 0.013 2 nm 4-22 E = K + U = mv 2 2 " ke 2 r . But mv 2 2 = 1 2 " # \$ % & ke 2 r . Thus E = 1 2 " # \$ % & ( ke 2 r " # \$ % & = U 2 , so U = 2 E = 2 " 13.6 eV ( ) = " 27.2 eV and K = E " U = " 13.6 eV " " 27.2 eV ( ) = 13.6 eV . 4-23 (a) r 1 = 0.052 9 nm ( ) n 2 = 0.052 9 nm (when n = 1 )

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(b) m e v = m e ke 2 m e r " # \$ % & m e = 9.1 ( 10 ) 31 kg ( ) 9 ( 10 9 Nm 2 2 ( ) 5.29 ( 10 ) 11 m * + , , - . / / ( 1.6 ( 10 ) 19 C ( ) M e v = 1.99 ( 10 ) 24 kg m s (c) L = m e vr = 1.99 " 10 # 24 kg m s ( ) 5.29 " 10 # 11 m ( ) , L = 1.05 " 10 # 34 kg m 2 s ( ) = h (d) K = E = 13.6 eV (e) U = " 2 K = " 27.2 eV (f) E = K + U = " 13.6 eV 4-25 (a) " E = hf = 13.6 eV ( ) 1 n f 2 # 1 n i 2 \$ % & ( ) or f = 13.6 eV ( ) 1 9 " 1 16 4.14 # 10 " 15 eV s \$ % & ( ) = 1.60 # 10 14 Hz
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hw5 - 4 4-1 4(a rn = n 2 h2 where n = 1 2 3 K me ke 2 rn =...

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