Before entering a mass spectrometer, ions pass through a velocity selector consisting of parallel plates separated by 1.6 mm and having a potential difference of 148 V. The magnetic field between the plates is 0.42 T. The magnetic field in the mass spectrometer is 1.2 T.

1)(a) Find the speed of the ions entering the mass spectrometer.

m/s
2)(b) Find the difference in the diameters of the orbits of singly ionized 238U and 235U. (The mass of a 235U ion is 3.903 x 10-25 kg.)

mm

1)   v = 2.20 10⁵ m / s , 2)  r = 4.86 10⁻³ m,    r = 4.92 10⁻³ m

Explanation:

1) A speed selector is a section where the magnetic and electrical forces have opposite directions, so

           q v B = q E

           v = E / B

           V = E s

           E = V / s

            v = V / s B

            v = 148 / (0.0016 0.42)

            v = 2.20 10⁵ m / s

2) when the isotopes enter the spectrometer, we can use Newton's second law

             F = m a

Acceleration is centripetal

             a = v² / r

             q v B = m v² / r

              r = m v / qB

The mass of uranium 235 is

           m = 3.903 10⁻²⁵ kg

The radius of this isotope is

             r = 3,903 10⁻²⁵ 2.20 10⁵ / (92  1.6 10⁻¹⁹  1.2)

             r = 4.86 10⁻³ m

The mass of the uranium isotope 238 is

              m = 238 a = 238 1.66 10-27 = 395.08 10-27 kg

The radius is

             r = 395.08 10⁻²⁷ 2.20 10⁵ / (92 1.6 10⁻¹⁹  1.2)

             r = 4.92 10⁻³ m

protons in

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