In a mass spectrometer chlorine ions of mass 35 u and charge +5 e are emitted fr
ID: 1622807 • Letter: I
Question
In a mass spectrometer chlorine ions of mass 35u and charge +5e are emitted from a source and accelerated through a potential difference of 250 kV. They then enter a region with a magnetic field which is perpendicular to their original direction of motion. The chlorine ions exit the spectrometer after being bent along a path with radius of curvature 3.5 m. What is the value of the magnetic field? (u = 1.66 ´ 10–27 kg, e = 1.6 ´ 10–19C)
Answer Choices:
A) 3.9 ´ 10–2 T
B) 2.5 ´ 10–2 T
C) 3.1 ´ 10–2 T
D) 5.4 ´ 10–2 T
E) none of the above
In a mass spectrometer chlorine ions of mass 35u and charge +5e are emitted from a source and accelerated through a potential difference of 250 kV. They then enter a region with a magnetic field which is perpendicular to their original direction of motion. The chlorine ions exit the spectrometer after being bent along a path with radius of curvature 3.5 m. What is the value of the magnetic field? (u = 1.66 ´ 10–27 kg, e = 1.6 ´ 10–19C)
Answer Choices:
A) 3.9 ´ 10–2 T
B) 2.5 ´ 10–2 T
C) 3.1 ´ 10–2 T
D) 5.4 ´ 10–2 T
E) none of the above
Explanation / Answer
Speed of chlorine particles will be:
KE = dU
0.5*m*v^2 = q*V
v = sqrt (2*q*V/m)
v = sqrt (2*5*1.6*10^-19*250*10^3/(35*1.67*10^-27))
v = 2.616*10^6 m/sec
Now using force balance
Fc = Fm
m*v^2/r = qvB
B = m*v/qr
B = 35*1.67*10^-27*2.616*10^6/(5*1.6*10^-19*3.5)
B = 5.46*10^-2 T
Correct option is D.
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