Question

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.

Answer 1

Answer:

0.0174  m

Explanation:

Given that:

mass of carbon 12 $m_{c \ 12} = 1.993 \times 10^{-26} \ kg$

mass of carbon 13 $m_{c \ 13} = 2.159 \times 10^{-26} \ kg$

Speed V = $7.50 \times 10^ 5 \ m/s$

$q = 1.6 \times 10^{-19 } \ C$

B = 0.9000 T

$R_1 = \dfrac{ m_{c \ 12} \ v}{ qB}$

$R_1 = \dfrac{ 1.993 \times 10^{-26} \ 7.50 \times 10^5}{ 1.6 \times 10^{-19} \times 0.90000}$

$R_1 =0.1038 \ m$

$R_2 = \dfrac{ m_{c \ 13} \ v}{ qB}$

$R_2= \dfrac{2.159 \times 10^{-26} \ 7.50 \times 10^5}{ 1.6 \times 10^{-19} \times 0.90000}$

$R_2 = 0.1125 \ m$

The spatial separation (D) = $2R_2 - 2R_1$

$D = 2(0.1125 \ m) - 2(0.1038 \ m)$

D = 0.0174  m