Positive ions from the source in a mass spectrometer enter a velocity selector r

Question

Positive ions from the source in a mass spectrometer enter a velocity selector region with crossed electric,   E = 1000 N/C, and magnetic fields, B = 0.16 T. The ions that go straight ahead enter a region where there is only a magnetic field, B = 0.16 T. The ions are singly ionized sodium ions with a mass m = 3.82x10-26 kg.

1. Determine the speed of the ions that go straight through the velocity selector.

2. On a diagram show how the electric field, the magnetic field, and the resulting velocity are related in space.

3. Determine the radius of the path of the ions once they enter the region with only a magnetic field.

(Any explanation or tips for clarity please, I want to understand not just get answers)

Explanation / Answer

a. apply E = Bv

speed v = E/B

v = 1000/0.16

v = 6250 m/s
------------------------------------------

c. KE = PE

0.5 mv^2 = eV

or v = sqrt(2eV/m)

v = sqrt(2*

apply centripetal force = magnetic force

i.e mv^2/r = qvB,

where m = mass o the charged particle

v = velocity,   r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now , r = mv/qB

r = 3.82 * 10^-26 * 6250/(1.6*e-19* 0.16)

r = 9.3261 mm

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