1.Suppose a carbon atom is ionized and given a net positive charge of 1 elementa

Question

1.Suppose a carbon atom is ionized and given a net positive charge of 1 elementary charge. The mass of the carbon ion is approximately 2x10-26 kg. If the positively charged ion is accelerated by falling through a potential difference of 10000 Volts and it then enters the magnetic field of a mass spectrometer answer the following questions:

a) What is the speed of the carbon after it has been accelerated in the potential? You can assume near zero initial velocity.

4x10^5 m/s

b) The path of the carbon ion is curved into a semicircular path and hits a photographic plate at a distance of 10 cm from the entrance slit of the spectrograph. What is the size of the magnetic field in Tesla inside the mass spectrometer to create this curvature? Note: the radius of the path is not 10 cm. Draw a diagram to see this and find the radius and B.

r=5 cm

B=0.0835 T

c) If the carbon ion is moving upward (in the plane of the page) and is bent into a counter clockwise path, which way is the magnetic field pointing? Explain using the right hand rule.

B into the page

Explanation / Answer

Part A)

By conservation of energy

PE = KE

qV = .5mv2

(1.6 X 10-19)(10000) = (.5)(2 X 10-26)(v2)

v = 4.0 X 105 m/s

Part B)

r = half the distance to exit

Half of 10 cm = 5 cm

Then apply r = mv/qB

.05 = (2 X 10-26)(4 X 105)/(1.6 X 10-19)(B)

B = 1.0 T

Part C)

By the right hand rule, the force is upward. Meaing place your palm upward. The direction of the charge is your thumb, to the right. That leaves your fingers pointing into the page. That is the direction of the B field.

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