Please show work and explain. Thanks. A mass spectrometer measures the mass of i
ID: 1452038 • Letter: P
Question
Please show work and explain. Thanks.
A mass spectrometer measures the mass of ions, by knowing their charge and the shape of the detector. If the Distance d between the entrance and exit holes is 7.50 cm and the B field has a value of 1.25 T, in the apparatus to the right, What velocity is needed to accelerate an O_2^+ with a mass of 32.0 u (u = atomic mass unit) and have it be detected? What potential difference is needed to reach this velocity? What potential is needed to detect H^+ with mass of 1.00 u? If this same potential from part c was used for the O^+_2 molecule, and the B field was turned on a split second after the it left the capacitor (thus allowing full cyclotron motion), what would the frequency of oscillation be?Explanation / Answer
a)
In a magnetic field
Fb = Fc
q*V*B = m*v^2/r
r = mv/qB
d = 2r = 2*mv/qB
0.075 = 2*32*1.66054*10^-26*v/(1.6*10^-19*1.25)
v = 1.411*10^4 m/s
___________
b)
work done = 0.5*m*v^2
dV*q = 0.5*m*v^2
dV*1.6*10^-19 = 0.5*32*1.66054*10^-26*(1.411*10^4)^2
dV = 330 V
++++++++++++++++
c
d = 2r = 2*mv/qB
0.075 = 2*1*1.66054*10^-26*v/(1.6*10^-19*1.25)
v = 4.52*10^5 m/s
dV*1.6*10^-19 = 0.5*1*1.66054*10^-26*(4.52*10^5)^2
dV = 10601.7 V
++++++++++++++
d)
r = mv/qB
T = 2pir/v = 2*pi*m*v/q*B*v = 2*pi*m/qB
f = 1/T = qB/(2*pi*m)
f = (1.6*10^-19*1.25)/(2*pi*32*1.66054*10^-26)
f = 59903 Hz