A) An alpha particle (q = 2e and m = 6.64e-27 kg) is accelerated from rest throu

Question

A) An alpha particle (q = 2e and m = 6.64e-27 kg) is accelerated from

rest through a potential difference of 1.2e+5 volts. Find the speed of the particle after being accelerated.

B) Assume that the magnetic field in the velocity selector is 0.8 T and out of the page , the velocity of the particle is along the +x-axis. The parallel plates of the velocity selector are 4 mm apart.

(i) Sketch the velocity selector showing the velocity v and the fields E and B.
(ii) Find the value of E (iii) the required voltage V' so that the selector allows ions with speed calculated in part (a) above to go through.

C) Find the radius of the path of the alpha particle. Assume that the uniform magnetic field B' in the main chamber is also 0.8 T and out of the page.

D) Find the time it takes to travel from the entrance slit to the exit slit.

Explanation / Answer

a)
Work done on alfa particle, W = q*V

w = 2*1.6*10^-19*1.2*10^5

= 3.84*10^-14 J

we know, W = 0.5*m*v^2

v =sqrt(2*W/m)

= sqrt(2*3.84*10^-14/6.64*10^-27)

= 3.4*10^6 m/s

C)

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

r = m*v/(B*q)

= 6.64*10^-27*3.4*10^6/(0.8*2*1.6*10^-19)

= 8.82*10^-2 m

= 8.82 cm

= 0.882 m

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