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A beam of singly ionized atoms of carbon...

A beam of singly ionized atoms of carbon (each charge +e) all have the same speed enters a mass spectrometer, as shown in Fig. The ions strike the photographic plate in two different locations 5 cm apart. The `._12C_6` isotope traces a path of smaller radius, `15.0 cm`. What is the atomic mass number of other isotope ?
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Let `R_1` be the radius of trajectory of the isotop `.^12C_6` and `R_2` that of the unknown isotope. The trajectory of the unknown isotope has a greater radius, and so the mass of the unknown isotop is greater than that of the `.^12C_6` isotop. From the figure provided in the question,
`d=2r=(2mv)/(qB)implies m prop d`
`(mA_2)/(mA_1)=(d_2)/(d_1)=(A_2)/12=35/30 implies A_2=14`
Thus, the unknown isotope is `.^14C_6`
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