Two isotopes of carbon carbon12 and carbon13 have masses of

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10-27 kg and 21.59 × 10-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 4.454 × 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.5385 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle. Use 1.602 × 10-19 C as the elementary charge and give your answer to four significant figures.

Solution

the spatial separation between the two isotopes:

         2[r₁₃ - r₁₂] = 2[v/Bq][m₁₃ - m₁₂]

                         = 2[4.454×10⁵/ 0.5385*1.602×10^-19][21.59 × 10^-27 -19.93 × 10^-27]

                         = 0.01714 m

                         = 1.7e-2 m