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

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 6.166 × 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.4009 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

Part A. for C-12

Using force balance

Fm = Fc

qvB = mv^2/r

So

r = mv/qB

Using given values:

r = 19.93*10^-27*6.166*10^5/(1.6*10^-19*0.4009)

r = 0.1916 T

diameter of circle will be, d1 = 2*0.1916 = 0.3832 m

Part B for C-13

Now in this case

r = mv/qB

r = 21.59*10^-27*6.166*10^5/(1.6*10^-19*0.4009)

r = 0.2075 m

d2 = 0.4150 m

Spatial difference = 0.4150 - 0.3832 = 0.0318

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