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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 7.50 10^5 m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.9000 T.

Required:
Determine the spatial separation between the two isotopes after they have traveled through a half-circle.

Respuesta :

ajeigbeibraheem

Answer:

0.0174  m

Explanation:

Given that:

mass of carbon 12 [tex]m_{c \ 12} = 1.993 \times 10^{-26} \ kg[/tex]

mass of carbon 13 [tex]m_{c \ 13} = 2.159 \times 10^{-26} \ kg[/tex]

Speed V = [tex]7.50 \times 10^ 5 \ m/s[/tex]

[tex]q = 1.6 \times 10^{-19 } \ C[/tex]

B = 0.9000 T

[tex]R_1 = \dfrac{ m_{c \ 12} \ v}{ qB}[/tex]

[tex]R_1 = \dfrac{ 1.993 \times 10^{-26} \ 7.50 \times 10^5}{ 1.6 \times 10^{-19} \times 0.90000}[/tex]

[tex]R_1 =0.1038 \ m[/tex]

[tex]R_2 = \dfrac{ m_{c \ 13} \ v}{ qB}[/tex]

[tex]R_2= \dfrac{2.159 \times 10^{-26} \ 7.50 \times 10^5}{ 1.6 \times 10^{-19} \times 0.90000}[/tex]

[tex]R_2 = 0.1125 \ m[/tex]

The spatial separation (D) = [tex]2R_2 - 2R_1[/tex]

[tex]D = 2(0.1125 \ m) - 2(0.1038 \ m)[/tex]

D = 0.0174  m