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25 Use the following information to answer the next question.
Cyclotron
A cyclotron is a particle accelerator that is constructed of two hollow metal shells
shaped like Ds in a perpendicular magnetic field created by magnets, as shown
below. The entire apparatus is placed in a vacuum. An alternating voltage is
maintained across the D separation. Positively charged particles such as protons
are injected near the centre of the Ds and travel in circular paths caused by the
external perpendicular magnetic field. The frequency of the alternating voltage is
adjusted to increase the speed of the particles each time they move across the Ds’
separation. Upper magnet
Injection
point Ds Path of protons D separation Lower magnet Cyclotron Specifications
Magnetic field intensity
Maximum voltage across D separation
D separation 0.863 T
20 000 V
5.00 cm Written Response — 15%
2. • Determine the direction of the magnetic field needed to cause protons
to circle in the direction shown. Justify your answer.
• Calculate the radius of the path of a proton travelling at 2.50 × 106 m/s.
• Calculate the speed of a proton after it passes once between the Ds, if it enters the
space between the Ds at 2.50 × 106 m/s.
26 Use the following information to answer the remainder of this question.
The speed of a particle moving with circular motion and the time it takes the
particle to complete one circular orbit are given by the formulas
v= 2π R
2π m
and T =
T
qB⊥ • Beginning with force equations from the tearout sheets, derive the formula for
the period
2π m
T=
qB⊥
• Show that the units of 2π m
are equivalent to seconds.
qB⊥ Clearly communicate your understanding of the physics principles that you
are using to solve this question. You may communicate this understanding
mathematically, graphically, and/or with written statements. 27 You have now completed the examination.
If you have time, you may wish to check your answers.
28 n = 1.00
c = 3.00 × 10 m/s Index of Refraction of Air................... Speed of Light in Vacuum .................. eV.s e = 1.60 × 10 Elementary Charge.............................. C –27
–31
–27
–27 mα = 6.65 × 10 m e = 9.11 × 10 m n = 1.67 × 10 m p = 1. 67 × 10 Alpha Particle ............... Electron ........................ Neutron ......................... Proton ........................... Rest Mass kg kg kg kg –11 m 2+ + 0 – p n e α Charge 7
RH = 1.10 × 10 1 Rydberg’s Constant for Hydrogen ...... Particles r1 = 5.29 × 10 Radius of 1st Bohr Orbit of Hydrogen
m J.s or 4.14 × 10 –34 h = 6.63 × 10 Planck’s Constant ............................... –15 J or –13.6 eV J E1 = – 2 .18 × 10 8 –19 –19 –18 Energy of an Electron in the 1st
Bohr Orbit of Hydrogen ..................... Atomic Physics 1 eV = 1.60 × 10 Electron Volt....................................... 2 2 Symbol –3 –6 –9 –12 deci .............. d ..................10 centi ............. c ................
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 Fall '09
 Quinlan
 Physics, Scientific Notation, Potential Energy, Magnetic Field, Atomic physics, .........

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