An alpha particle has a mass of 6.23 × 10 −27 kg and bears a double elementary positive charge. Such a particl?
An alpha particle has a mass of
6.23 × 10
−27
kg and bears a double elementary positive charge. Such a particle is observed to move through a 3.4 T magnetic field
along a circular path of radius 0.18 m.
The charge on a proton is 1.60218×10
−19
C.
What speed does it have?
Answer in units of m/s
What is its kinetic energy?
Answer in units of J
What potential difference in MV would be
required to give it this kinetic energy?
Answer in units of MV
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Verified answer
The magnetic force
Fm = qvB provides the centripetal force
qvB = mv^2/R
qB = mvR
v = qBR/(m)
with mass = 6.23*10^-27 kg
q = 3.204*10^-19 C
R = 0.18 m
B = 3.4 T
v = 3.204*10^-19*3.4*0.18/6.23*10^-27
v = 31474285 m/s
v = 3.147*10^7 m/s
-----------
kinetic energy Ek is
Ek = 1/2 mv^2
Ek = 1/2*6.23*10^-27*(3.147*10^7)^2
Ek = 3.0849*10^-12 J
----------
Potential difference V is
V = Ek/q
V = 3.0849*10^-12/3.204*10^-19
V = 9 628 508 Volt
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