Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 × 10 -27 k

Question

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 4.103 × 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.4368 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.

Explanation / Answer

formula m=qBr/v

Apply above formula for both isotopes by calculating r. They are going to move along different circles coz they have different masses. In half-circle they are going to be 2(r2-r1) meters apart (diameter difference of the 2 circles.)

We get r1 = 117.01 x 10-3m and r2 = 126.76 x 10-3m

So spatial separation = 19.5 x 10-3m or .019 metres

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