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matrenka [14]
3 years ago
12

Medical cyclotrons need efficient sources of protons to inject into their center. In one kind of ion source, hydrogen atoms (i.e

., protons with one orbiting electron) are fed into a chamber where there is a strong magnetic field. Electrons in this chamber are trapped in tight orbits, which greatly increases the chance that they will collide with a hydrogen atom and ionizes it. One such source uses a magnetic field of 90 mT, and the electrons' kinetic energy is 2.0 eV.If the electrons travel in a plane perpendicular to the field, what is the radius of their orbits?
Physics
1 answer:
blondinia [14]3 years ago
3 0

Answer:

Explanation:

Electron's kinetic energy = 2 eV

= 2 x 1.6 x 10⁻¹⁹ J

1/2 m v² = 3.2 x 10⁻¹⁹

1/2 x 9.1 x 10⁻³¹ x v² = 3.2 x 10⁻¹⁹

v² = .703 x 10¹²

v = .8385 x 10⁶ m/s

Electrons revolve in a circular orbit when forced to travel in a magnetic field whose radius can be expressed as follows

r = mv / Bq

where m , v and q are mass , velocity and charge of electron .

here given magnetic field B = 90 mT

= 90 x 10⁻³ T

Putting these values in the expression above

r =  mv / Bq

= \frac{9\times10^{-31}\times.8385\times10^6}{90\times10^{-3}\times1.6\times10^{-19}}

= .052 mm.

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