15. A mass spectrometer measures the mass of ions, by knowing their charge and t

Question

15. 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.

a. What velocity is needed to accelerate an O2 + with a mass of 32.0 u (u = atomic mass unit) and have it be detected?

b. What potential difference is needed to reach this velocity?

c. What potential is needed to detect H+ with mass of 1.00 u?

d. If this same potential from part c was used for the O2 + 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?

Please show work and explain! Thank you!

Explanation / Answer

for charge particle in magnetic field

mv2 / r = qvB

v=qBr / m

where q= charge of the particle

B= magnetic field= 1.25 T (given)

r =radius of the circular path = d / 2 =7.50 /2 cm = 3.75 cm = 3.75 x 10-2 m

m= mass of the particle

mass of the O2+ = 32.0 U = 32.0 / (6.02 x 1023) g =5.32 x 10-23 g

hence velocity of the O2+ = (1.6 x 10-19 ) x 1.5 x (3.75 x 10-2) /( 5.32 x 10-23) ms-1

= 1.7 x 102 ms-1 ................ans

let V is the reqired potential then,

eV=mv2 / 2

V= mv2 / 2e

=( 5.32 x 10-23) x (1.7 x 102)2 / 2 x 1.6 x 10-19

= 4.8 V .........................ans

mass of the H+ = 1.0 U = 1.0 / (6.02 x 1023) g = 1.7 x 10-24 g

hence velocity of the H+ = (1.6 x 10-19 ) x 1.5 x (3.75 x 10-2) /( 1.7 x 10-24) ms-1

= 5.3 x 103 ms-1

hence needed potential to dectect H+ =  mv2 / 2e

=( 1.7 x 10-24) x (5.3 x 103)2 / 2 x 1.6 x 10-19

= 1.5 x 102 V ................ans

if part c potential is used for O2+ , then velocity of O2+ is given by

v2 = 2eV / m

= 2 x 1.6 x 10-19 x 1.5 x 102 /  5.32 x 10-23

= 9 x 105

hence v = (9 x105)0.5

= 9.5 x 102  ms-1

frequency of oscillation is given by

f = v / 2r

= ( 9.5 x 102) / (2 x 3.14 x 3.75 x 10-2)  s-1

= 403 s-1 ....................ans

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