Two singly ionized ions move out of a slit at point S and into a magnetic field

Question

Two singly ionized ions move out of a slit at point S and into a magnetic field of magnitude 0.100T pointing into the page. Each has a speed of 1.0 x 10^6 m/s. The nucleus of the first atom contains one proton and had a mass of 1.67 x 10^-27 kg, whereas the nucleus of the second atom contains a proton and a neutron and has a mass of 3.34 x 10^-27 kg. Atoms with the same number of protons in the nucleus but different masses are called isotopes. The two isotopes here are Hydrogen and Deuterium. Find their distance of separation when they strike a photo-graphic plate at P.

Explanation / Answer

m v^2/R = q v B

m v/R = q B

R = mv/qB

distance of separation = R2 - R1 = m2 - m1 * (v/qB)

= (3.34e-27-1.67e-27)*(1e6/(1.6e-19*0.1))

= 0.104375 m

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