The diagram on the left shows an arrangement used to measure the masses Of ions.

Question

The diagram on the left shows an arrangement used to measure the masses Of ions. An ion of mass m and charge q is produced essentially at rest as rest source S. The ion is accelerated by a potential difference of V volts and allowed to enter the magnetic field B. In the field it moves in a semicircle, striking a photographic plate at a distance x from the entry slit. The ion inters the magnetic ut a velocity of 1.7 times 10^6 m/s. The mass of the ion is 1.06times 10-26 kg. Calculate the value of x. the diameter of the circular path of the ion in the in the magnetic field B. b) Through What potential difference must the ion be accelerated in order to obtain a a velocity of 1.7 times 10^-6 m/s.

Explanation / Answer

a)

v=1.7x10^6m/s; m=1.06x10^-26kg; B=1.5T; q=1.602x10^-19C

x, which is also the diameter of the circular trajectory, can be calculated using Newton's second law F=m*a

q*v*B=m*v^2/R...R=m*v/qB=1.06x10^-26kg*1.7x10^6m/s/1.602x10^-19C*1.5T=0.075m

Thus, R=x/2, x=2R=0.15m=15cm

b) Kf = 0.5 m*v2 = q *V.

V=0.5*1.06x10^-26kg*(1.7x10^6m/s)^2/1.602x10^-19C=95611.73 eV

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