i need the final answers ( numbers i put in box + unit ) plz . Chapter 28, Probl

Question

i need the final answers ( numbers i put in box + unit ) plz .

Chapter 28, Problem 027 A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 × 10-25 kg and charge 3.20 10-19 C from related species. The ions are accelerated through a potential difference of 86.4 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.35 m. After traveling through 180° and passing through a slit of width 1.28 mm and height 0.869 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 1.07 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 0.819 h. Detector (a) Number (b) Number (c) Number Units Units Units

Explanation / Answer

given

mass of Uranium = m = 3.92 X 10-25 kg

charge of the Uranium = q = 3.2 X 10-19 C

V = 86.4 kV = 86400 V

a )

using equations F = m v2 / r = q V

v = ( 2 q V / m )1/2

= ( 2 X 3.2 X 10-19 X 86400 / 3.92 X 10-25 )1/2

= 11.87 X 106 m/sec

using B = m v / q r

B = 3.92 X 10-25 X 11.87 X 106 / 3.2 X 10-19 X 1.35

B = 10.77 T

b )

I = q M / m

= ( 3.2 X 10-19 X 1.07 X 10-6 / 0.819 X 3600 / 3.92 X 10-25 )

= 2.962 X 10-4 A

c )

E = I dV t

= 2.962 X 10-4 X 86400 X 0.819 X 3600

= 75454.509 J

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