15. The device shown above (a spectrometer) accelerates an ion from rest through

Question

15. The device shown above (a spectrometer) accelerates an ion from rest through a potential difference E = 800 V between two parallel plates as shown above. The ion has a charge of magnitude 2e. The ion then enters a region containing a uniform magnetic field B = 0.075 T which is constant in magnitude and perpendicular to the plane of the path of the ion. The particle curves in a semicircular path and strikes a detector as shown above. The mass of the ion is 6.64 X 10-27 kg. Recall that e = 1.602 X 10-19 C. (25 points)

Explanation / Answer

Apply q*V = 0.5*m*v^2

2*1.6*10^-19 * 800 = 0.5*6.64*10^-27*v^2

v = 27.76*10^4 m/s

radius r = m*v/(q*B) = (6.64*10^-27*27.76*10^4)/(2*1.602*10^-19*0.075) = 76.7 mm

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