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 6.50 105 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.5700 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle.

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Khoso123 Khoso123 · Answer 1 · 2020-03-17T02:36:05+01:00

Answer:

d=0.024m

Explanation:

The mass of the isotopes are

[tex]m_{c12}=1.993*10^{-26}kg[/tex]

[tex]m_{c13}=2.159*10^{-26}kg[/tex]

The velocity of isotopes are [tex]v=6.50*10^{5}m/s[/tex]

Charge q=+e=1.6×10⁻¹⁹C and the magnetic field is B=0.5700T

The radius of circular paths for isotopes are:

[tex]r_{1}=\frac{m_{c12}*v}{|q|B} \\r_{1}=\frac{1.993*10^{-26}kg*6.50*10^{5}m/s}{1.6*10^{-19}C*0.5700T}\\ r_{1}=0.142m[/tex]

[tex]r_{2}=\frac{m_{c13}*v}{|q|B} \\r_{2}=\frac{2.159*10^{-26}kg*6.50*10^{5}m/s}{1.6*10^{-19}C*0.5700T}\\ r_{2}=0.154m[/tex]

So the spatial separation between two isotopes given as:

d=2r₂-2r₁

d=2(0.154)-2(0.142)

d=0.024m