1) Two types of singly ionized atom having the same charge q but masses that dif
ID: 2008165 • Letter: 1
Question
1) Two types of singly ionized atom having the same charge q but masses that differ by a small amount ?m are introduced into the mass spectrometer described in Sample Problem 29-3.Calculate ?x for a beam of singly ionized chlorine atoms of masses 35 and 37 u if V = 8.9 kV and B = 0.79 T.
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2)Neutral Particle A neutral particle is at rest in a uniform magnetic field B. At time t = 0 it decays into two charged particles, each of mass m.
The two particles move off in separate paths, both of which lie in the plane perpendicular to B. At a later time the particles collide. Express the time from decay until collision in terms of m, B, and q
Explanation / Answer
Given masses of two atoms m1 = 35 u = 35 ( 1.6 *10 -27 kg ) m2 = 37 u = 37 ( 1.6 *10 -27 kg ) charge on each atom q = 1. 6 *10 -19 C magnitude of magnetic field B = 0.79 T potential difference across the spectrometer is V = 8.9 kV magnetic force on atom due to magnetic field is m v 2 / r = Bq v radius of circular path is r = m v / Bq velocity of atom 1 is ( 1/2) m1 v 12 = V * q v1 2 = ( 8.9*103 V ) (1. 6 *10 -19 C ) 2 / 35 ( 1.6 *10 -27 kg ) = 0.05085*1012 v1 = 0.2255*106 m/s raidus of circular path formed by atom1 is r 1 = (35 ( 1.6 *10 -27 kg ) )(0.2255*106 m/s ) / ( 0.79)(1.6 *10 -19 kg ) = 9.99*10-2 m velocity of atom 2 is ( 1/2) m1 v 22 = V * q v2 2 = ( 8.9*103 V ) (1. 6 *10 -19 C ) 2 / 37 ( 1.6 *10 -27 kg ) = 0.0481*1012 v2 = 0.2193*106 m/s raidus of circular path formed by atom1 is r 2 = (37 ( 1.6 *10 -27 kg ) )(0.2193*106 m/s ) / ( 0.79)(1.6 *10 -19 kg ) = 10.27*10-2 m there fore x = r 2 - r 1 = 10.27*10-2 m - 9.99 *10-2 m = 0.28*10-2 m 2) A charged particle when enters into perpendicular to the magnetic field, it traces a circualr path. Because both are oppositely charged particles, they will move in the cirular path but in opposite direction, i,e, if one move in clock wise direction , then the other will move in the counter clock wise direction .Thus before they collide from thier inital point , they will trace a full circle of radius r (say) . velocity of atom 2 is ( 1/2) m1 v 22 = V * q v2 2 = ( 8.9*103 V ) (1. 6 *10 -19 C ) 2 / 37 ( 1.6 *10 -27 kg ) = 0.0481*1012 v2 = 0.2193*106 m/s raidus of circular path formed by atom1 is r 2 = (37 ( 1.6 *10 -27 kg ) )(0.2193*106 m/s ) / ( 0.79)(1.6 *10 -19 kg ) = 10.27*10-2 m there fore x = r 2 - r 1 = 10.27*10-2 m - 9.99 *10-2 m = 0.28*10-2 m 2) A charged particle when enters into perpendicular to the magnetic field, it traces a circualr path. Because both are oppositely charged particles, they will move in the cirular path but in opposite direction, i,e, if one move in clock wise direction , then the other will move in the counter clock wise direction .Thus before they collide from thier inital point , they will trace a full circle of radius r (say) . there fore x = r 2 - r 1 = 10.27*10-2 m - 9.99 *10-2 m = 0.28*10-2 m 2) A charged particle when enters into perpendicular to the magnetic field, it traces a circualr path. Because both are oppositely charged particles, they will move in the cirular path but in opposite direction, i,e, if one move in clock wise direction , then the other will move in the counter clock wise direction .Thus before they collide from thier inital point , they will trace a full circle of radius r (say) . Because both are oppositely charged particles, they will move in the cirular path but in opposite direction, i,e, if one move in clock wise direction , then the other will move in the counter clock wise direction .Thus before they collide from thier inital point , they will trace a full circle of radius r (say) . magnetic force on atom due to magnetic field is m v 2 / r = Bq v radius of circular path is r = m v / Bq time period T = 2 r / v = ( 2 / v ) ( m v / Bq ) = 2m / Bq As per rules please post one question per one post m v 2 / r = Bq v radius of circular path is r = m v / Bq time period T = 2 r / v = ( 2 / v ) ( m v / Bq ) = 2m / Bq As per rules please post one question per one postRelated Questions
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