2) 20 pts. A stream of singly charged selenium ions (\"+1.6x10-19C) moves throug

Question

2) 20 pts. A stream of singly charged selenium ions ("+1.6x10-19C) moves through a mass spectrometer, as shown. These ions first pass through a velocity selector, with electric field 1.00 x 10 V/m toward the right and magnetic field 0.500 T out of the page. The ions then pass into a deflection chamber, again with magnetic field 0.500 T out of the page (but without an electric field). The ions hit the detector (a photographic plate) after traveling on a path with radius 30.0 cm in the deflection chamber. Find the mass of the selenium ions. S, Photographic plat?

Explanation / Answer

The magnetic force on a moving charged particle is given by

F= qvB = mv2/r

where. qvB is the magnetic force

and

mv2/r is the centripetal force. these two balance

thus,

B = mv/qr

where,

m = mass of ions

v = velocity of ions

q = charge = 1.6 x 10-19 C

r = radius = 30.0 cm = 0.30 m

The electric field is perpendicular to the velocity of ions and exerts a force F = qE on the ions.

The magnetic field is perpendicular to both the ion velocity and the electric field. the magnetic force has a magnitude

F = qvB, and is in opposite direction to electric field. the forces balance, means

qE = qVB

or v = E/B

given that E = 1.00 x 105 V/m

B = 0.500 T

hence

v = (1.00 x 105 )/0.500 = 2 x 105 m/s

thus, the mass of the ions is

m = qBr/v = (1.6 x 10-19) (0.500)(0.30)/(2 x 105) = 0.12 x 10-24 = 1.2 x 10-25 kg

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