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

0.0174 m

Step-by-step explanation:

Given that:

mass of carbon 12
`m_(c \ 12) = 1.993 * 10^(-26) \ kg`

mass of carbon 13
`m_(c \ 13) = 2.159 * 10^(-26) \ kg`

Speed V =
`7.50 * 10^ 5 \ m/s`

`q = 1.6 * 10^(-19 ) \ C`

B = 0.9000 T

`R_1 = ( m_(c \ 12) \ v)/( qB)`

`R_1 = ( 1.993 * 10^(-26) \ 7.50 * 10^5)/( 1.6 * 10^(-19) * 0.90000)`

`R_1 =0.1038 \ m`

`R_2 = ( m_(c \ 13) \ v)/( qB)`

`R_2= (2.159 * 10^(-26) \ 7.50 * 10^5)/( 1.6 * 10^(-19) * 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