Mass Spectrometer 01 Due in 12 hours, 59 minutes An electric potential is set up

Question

Mass Spectrometer 01 Due in 12 hours, 59 minutes An electric potential is set up across a pair of parallel plates such that the left plate is at-412 V and the righe plate g·OL An-retron- re set here there is a magnetic f and accelerates towards the right plate. When it reaches the right plate, it passes through a small hole and enters a region w strength 6.040x to7 T pointing into the paper. The electron travels in a semi-circular arbit and hits a detector a distance, d, fromm the point the region of the magnetic field. See the figure below What is the kinetic energy of the electron when it reaches the hole in the right plate? Subenit Answer Tries o/1o What is the speed of the electron as it passes through the hale? Submit Angwer Tries D/10 What distance, d, will place the detector at the appropriate position to detect the electron? Submit Anawer Tries 0/10 11:00 AM

Explanation / Answer

here,

magnitude of magnetic feild , B = 6.04 * 10^-3 T

the potential difference , dV = 0 - 412 V = 412 V

mass of electron , m = 9.1 * 10^-31 kg

charge on electron , q = 1.6 * 10^-19 C

a)

using work energy theorm

the kinetic energy of electron , Ke = work done by potential

Ke = dV * q

Ke = 420 * 1.6 * 10^-19 J

Ke = 6.72 * 10^-17 J

b)

let the speed of electron be v

Ke = 0.5 * m * v^2

6.72 * 10^-17 = 0.5 * 9.1 * 10^-31 * v^2

v = 1.22 * 10^7 m/s

c)

the distance , d = 2 * radius of orbit

d = 2 * m * v /( q * B)

d = 2 * 9.1 * 10^-31 * 1.22 * 10^7 /( 1.6 * 10^-19 * 6.04 * 10^-3) m

d = 2.3 * 10^-2 m

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