PC Chapter 04

PC Chapter 04 - 4 The Particle Nature of Matter 4-1 F...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
47 4 The Particle Nature of Matter 4-1 F corresponds to the charge passed to deposit one mole of monovalent element at a cathode. As one mole contains Avogadro’s number of atoms, - = × 19 23 96 500 C 1.60 10 C 6.02 10 e . 4-2 (a) Total charge passed (29 ( 29 = == * 1.00 A 3 600 s 3 600 C it . This is - × 22 19 3 600 C 2.25 10 1.60 10 C electrons. As the valence of the copper ion is two, two electrons are required to deposit each ion as a neutral atom on the cathode. The number of Cu atoms = 22 number of electrons 1.125 10 Cu 2 atoms. (b) So the weight (mass) of a Cu atom is: - × 22 22 1.185 g 1.05 10 g 1.125 10 atoms . (c) = molar weight 2 96 500 mq or ( ( ( = 22 molar weight 96 500 1.185 g 96 500 C 63.53 g 3 600 C m q . 4-3 Thomson’s device will work for positive and negative particles, so we may apply θ 2 q V m B ld . (a) ( ( θ - = × 7 2 0.20 radians 2 000 V 0.10 m 0.02 m 9.58 10 C kg 4.57 10 T q V m B ld (b) As the particle is attracted by the negative plate, it carries a positive charge and is a proton. - -  × =  ×  19 7 27 1.60 10 C 9.58 10 C kg 1.67 10 kg p q m
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
48 CHAPTER 4 THE PARTICLE NATURE OF MATTER (c) ( 29 - = = = × 26 2 000 V 4.57 10 T 2.19 10 m s d 0.02 m x EV v BB (d) As ~ 0.01 x vc there is no need for relativistic mechanics. 4-4 ( 29    = ===       2 22 2 1 1 111 2 222 y ex Fl E e l V el y at mv d ( 29 ( 29 θ = = = == =+= + 2 2 12 2 1 tan 2 yy x x e x xe x e x Dv Da t E Ve l y D DD v v m v v dm v V e ll yyy d mD v Solving for e e m yields = + 2 2 x v I l e de y V Dm or = + 2 1 2 x e yvd e m V lD . 4-5 (a) Draw the curved path of the electron as follows: - += 2 r y lr - + += + = 2 2 2 2 r r y ylr ly r y y r l r r – y (b) ( 29 - = = ×= 48 1 060 V 2.5 10 m 2.39 10 m s 0.795 0.017 7 V Bd . Using the classical expression p mv Bre gives ( ( -- × = = × 8 31 19 2.39 10 m s 9.11 10 kg 1.60 10 C 0.076 9 m 0.017 7 T mv r Be . To find the value of y corresponding to this r use 20 y r yl or - - +×= 24 0.153 8 6.10 10 0 . Using the quadratic formula, ( ( 29 ( - - =-±   = + ±= 2 2 4 4 2 0.153 8 4 6.101 10 0.153 8 0.150 m 2 b ac yb a y - 3 4.08 10 m 0.004 08 m (the first answer is discarded because ry ). Using the relativistic expression γ p mv Bre gives
Background image of page 2
MODERN PHYSICS 49 (29 ( 29 ( ( ( γ - - ×× = ==   3 18 12 19 2 1 9.11 10 kg 2.39 10 m s 0.126 7 m 1 0.795 0.017 7 T 1.60 10 C me r Be . The y values corresponding to this r value are found from - - + ×= 24 0.253 6.10 10 0 yy or = 0.251 m y , 0.002 43 m . Discarding the first answer because r must be greater than y , leaves = 0.002 43 y m in good agreement with ( 29 observed 0.002 4 0.000 5 m y . 4-6 The velocity of fall - = = 4 0.004 m 2.52 10 m s 15.9 s y v t . (a) The radius, a , is given by ( ( ( ( η ρ -- -  = =   54 6 32 9 1.81 10 kg m s 2.52 10 m s 9 1.62 10 m 2 2 800 kg m 9.81 m s v a g . The mass, m , is given by ( 29 ( 29 ( 29 ρ ρ ππ = × 3 3 3 6 14 4 1.33 800 kg m 1.62 10 m 1.42 10 kg 3 m Va . (b) ( + = 1 1 mg E vv q v where v is the velocity of fall and v is the velocity of rise. The electric field is given by = 4 000 V 200 000 V m 0.020 0 m V E d , - 4 2.52 10 m s v , - = 4 1 0.004 m 1.11 10 m s 36.0 s v , - 4 2 2.31 10 m s v , - 4 3 1.67 10 m s v , - 4 4 3.51 10 m s v , - 4 5 5.31 10 m s v ( - - - - - - ×+ + = = + = 19 19 1 1 19 2 2 19 3 19 4 19 5 6.97 10 C 2.52 1.11 10.0 10 C 2.52 13.4 10 C 11.6 10 C 16.7 10 C 21.6 10 C mg vv q Ev q q q q
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
50 CHAPTER 4 THE PARTICLE NATURE OF MATTER (c) By inspection we choose integers that will yield an elementary charge between 1.5 and - × 19 2.0 10 C - - - - - 19 1 19 2 19 3 19 4 19 5 1.67 10 C 6 1.68 10 C 8 1.66 10 C 7 1.67 10 C
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 20

PC Chapter 04 - 4 The Particle Nature of Matter 4-1 F...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online