Download Answers to Cyclotron Questions File

Background
In a cyclotron, protons are
kept moving in a circular
path by a uniform magnetic
field at right angles to the
plane of the path.
protons in
circular path
uniform
B-field
Only a few centimetres in
diameter, the Lawrence
cyclotron accelerated protons to
energies of 80 keV.
mass of proton = 1.7 x 10–27 kg
charge on proton = 1.67 x 10–19 C
1.
using
so
What is the velocity of a proton with an energy of 80 keV?
1 2
KE  mv
2
2  80 10 1.6 10
v
27
1.67 10
2E
v
m
Remembering that 1 eV =1.6 x 10-1 9J
80keV = (80 x 103 x 1.6 x10-19)
3
v =3.9 x106ms-1
19
2..The largest possible path had a radius of about 50 mm.
What strength of magnetic field must have been used?
r =50mm
The centripetal force (mv2/r) is provided by the force on the proton due to
the magnetic field (BqV)
2
mv
F
 Bqv
r
r = 50mm ( the path radius )
2
mv
 Bvq
r
mv
B
qr
27
1.67 10  3.88 10
B
19
3
1.6 10  50 10
B  0.82T
6
3.What would be the radius of the path followed by a
proton with half this maximum energy in the same field?
Because we know the energy we can calculate the new
velocity of the proton. Its energy is half the original so its
velocity is.
v
KE1
2
mv
r
QB
1.67 1027  3.88 106
r
 0.036m
19
3
1.6 10  0.82 10  2
How long would it take 80 keV protons to travel once round their
path? How long would it take for those with half this energy?
Circular motion theory gives us
T
2

and as
  vr
2 r 2  50 103
8
T


8.1

10
s
6
v
3.88 10
from 3
mv
r
, r  const  v
QB
and T is the same for all velocities
and hence all particle energies
Constructed of two D -shaped chambers (later called ‘dees’ because of
their shape), the cyclotron worked by giving particles of any energy, on
their respective paths, a push every time they had completed half an
orbit.
push
push
beam of protons
5. How was it possible for particles of differing energy all to be accelerated
together?
We have just seen that the time taken for an orbit is independent of
its energy so particles of different energies will orbit at the same
speed e the same mass and chargeprovided that they hav