Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 Two isotop

Question

Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93

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 4.717 ? 10^5 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is0.6707 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

by using formula for radius r = mv/qB

now r1 for carbon 12

r1 = 19.93*10^-27*4.717*10^5/(0.6707*1.602*10^-19 ) = 0.0874 m

now r2 for carbon 13

r2 = 21.59*10^-27*4.717*10^5/(0.6707*1.602*10^-19 ) = 0.0947 m

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.)

ans is 2 * (0.0947 - 0.0874) = 0.0146 m

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