Question

You have been asked to review a new apparatus, which is proposed for use at a new semiconductor ion implantation facility. One part of the apparatus is used to slow down He ions which are positive and have a charge twice that of an electron (He++). This part consists of a circular wire that is charged negatively so that it becomes a circle of charge. The ion has a velocity of 200 m/s when it passes through the center of the loop of charge on a trajectory perpendicular to the plane of the circle. The circle has a charge of 7 nC and radius of 8.0 cm. The sample with which the ion is to collide will be placed 2.5 mm from the charged circle. To check if this device will work, you are asked to calculate the distance from the circle that the ion goes before it stops. To do this calculation, you assume that the circle is very much larger than the distance the ion goes and that the sample is not in place. Will the ion reach the sample? If not, suggest at least two quantitative changes to the apparatus or set up so that it does reach the sample. You look up the charge of an electron and mass of the helium in your trusty Physics text to be 1.6 x 10-19 C and 6.7 x 10-27 Ka.

Answer 1

Answer: from energy conservation, Toidal mechanical energy - k9,22 + M Final mechanical energy = K2,22 to V VR²+12 hitz + 2 m he lo? = K2122 VR²+r2 VRAESTR = Bitment - +1-727 K2 PL2 + I mielo? = K2,22 ( 1 - 1 ] K2:22 + & mules = K2:22 - K2,2,312 2R3 me lo = - K2,22512 given, r= ( mHeR² 1/2 IR=8x10²m l-K2, 22 | 2, (charge of ion) = r=/6.7x1027x512x100 % 2x1.6x109 9x109 x 3.2x109 x 7x109 ) x 200 22 = 78109 Im He = 6.7x1827kg V = 200m/s R R3 r=13.4304 x 1030 1/2 ( 2.016 xio17 ) X 200 = (1.7015 xjö 3 ) "2 x 200 0 = 4,125x10° x 200 r = 8.25 x105m = 8-25 xiomm it velocity of ion is increased by 1000 times or change of ring is reduced by 100 times. so charge will not reach the target