Two isotopes of carbon, carbon-12 and carbon-13, have masses of 1.993 10-26 kg and 2.159 10-26 kg, respectively. These two isotopes are singly ionized ( e) and each is given a speed of 7.13 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.5100 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle.

d = 0.030 m

Explanation:

The radius of curvature (r) of the two isotopes can be calculated using the following equation:

Where:

The radius of the isotope carbon-12 is:

Simimlarly, the radius of the isotope carbon-13 is:

Finally, the spatial separation between the two isotopes after they have traveled through a half-circle () is:

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