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hw5 - 4 The Particle Nature of Matter 4-14(a n 2 2 rn 2...

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4 The Particle Nature of Matter 4-14 (a) r n n 2 2 m e ke 2 ; where n 1, 2, 3, r n n 2 1.055 10 34 Js 2 9.11 10 31 kg 9.0 19 9 Nm 2 C 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 0.212 1 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 C 2 1.60 10 19 C 2 9.11 10 31 kg 0.052 9 10 9 m 1 2 2.19 10 6 m s v 2 1.09 10 6 m s v 3 7.28 10 5 m s (c) As c 3.0 10 8 m s , v  c and no relativistic correction is necessary. 4-15 (a) The energy levels of a hydrogen-like ion whose charge number is 2 is given by E n   13.6 eV Z 2 n 2 54.4 eV n 2 for Z 2 . He 0 E 3   6.04 eV E 2   13.6 eV So E 1   54.4 eV E 2   13.6 eV E 3   6.04 eV , etc. E 1   54.4 eV
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(b) For He , Z 2 so we see that the ionization energy (the energy required to take the electron from the state n 1 to the state n   is E   13.6 eV 2 2 1 2 54.4 eV n 2 for Z 2 . He 4-16 For Li 2 , Z 3 from Equation 4.36 0 E 3   13.6 eV E n   13.6 Z 2 n 2 eV   122.4 n 2 eV E 2   30.6 eV So E 1   122.4 eV E 2   30.6 eV E 3   13.6 eV , etc. E 1   122.4 eV 4-17 r n 2 2 Zm e ke 2 n 2 Z 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
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