The electrons in a beam are moving at 2.8 × 108 m/s in an electric field of 2500

Question

The electrons in a beam are moving at 2.8 × 108 m/s in an electric field of 25000 N/C. What value must the magnetic field have if the electrons pass through the crossed fields undeflected. 4. A mass spectrometer consists of an accelerating potential to give the partical velocity before entering a uniform magnetic field. The mass spectrometer using a beam of doubly ionized sodium atoms has the following settings: the magnetic field is 0.0975 T; the charge of an atom is 3.20 × 10-19 C; .the radius of the orbit is 0.080 m; and the potential difference is 150 V. Calculate the mass of a sodium atom

Explanation / Answer

3. given

v = 2.8*10^8 m/s

electrons

E = 25,000 N/C

B = ?

for undeflected beam, from force balance

qvB = qE

B = E/v = 25,000/2.8*10^8 = 8.92857*10^-5 T

4. given

doubly ionised sodium ions

q = 2e

B = 0.0975 T

q = 3.2*10^-19 C

r = 0.08 m

V = 150 V

m = ?

hence

from force balance

mv^2/r = qvB

m = rqB/v

now, 0.5mv^2 = qV

v = sqrt(2qV/m)

hence

m = rB*sqrt(mq/2V)

sqrt(m) = r*B*sqrt(q/2V)

m = r^2*B^2*q/2V

m = 6.4896*10^-26 kg

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