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A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.2 T What is the diameter of the largest orbit, just before the protons exit the cyclotron?

Respuesta :

Answer:

diameter of largest orbit is 0.60 m

Explanation:

given data

isotopes accelerates KE = 6.5 MeV

magnetic field B = 1.2 T

to find out

diameter

solution

first we find velocity from kinetic energy equation

KE = 1/2 × m×v²   ........1

6.5 × 1.6 × [tex]10^{-19}[/tex] = 1/2 × 1.672 × [tex]10^{-27}[/tex] ×v²

v = 3.5 × [tex]10^{7}[/tex] m/s

so

radius will be

radius = [tex]\frac{m*v}{B*q}[/tex]   ........2

radius =  [tex]\frac{1.672*10^{-27}*3.5*10^{7}}{1.2*1.6*10^{-19}}[/tex]  

radius = 0.30

so diameter = 2 × 0.30

so diameter of largest orbit is 0.60 m

Lanuel

The diameter of the largest orbit, just before the protons exit the cyclotron is equal to 0.614 meter.

Given the following data:

  • Potential difference = 6.5 MeV
  • Magnetic field, B = 1.2 T

Scientific data:

  • Mass of proton = [tex]1.67 \times 10^{-27}\;kg[/tex]
  • Charge of proton = [tex]1.6 \times 10^{-19}\;C[/tex]

To calculate the diameter of the largest orbit, just before the protons exit the cyclotron:

First of all, we would determine the velocity of protons.

According to the law of conservation of energy, the work done in accelerating the proton is equal to the kinetic energy of the proton possesses. Mathematically, this is given by this expression:

[tex]qV_d = \frac{1}{2} MV^2[/tex]

Where:

  • q is the charge of proton.
  • [tex]V_d[/tex] is the potential difference of proton.
  • M is the mass of proton.
  • V is the velocity of proton.

Making V the subject of formula, we have:

[tex]V=\sqrt{\frac{2qV_d}{M} }[/tex]

Substituting the given parameters into the formula, we have;

[tex]V=\sqrt{\frac{2 \times 1.6 \times 10^{-19}\times \;6.5 \times 10^6 }{1.67 \times 10^{-27}} }\\\\V=\sqrt{\frac{2.08 \times 10^{-12} }{1.67 \times 10^{-27}}}\\\\V=\sqrt{1.25 \times 10^{15}}\\\\V=3.53 \times 10^7\;m/s[/tex]

In a magnetic field, diameter is given by this formula:

[tex]Diameter = \frac{2MV}{Bq} \\\\Diameter = \frac{2 \times 1.67 \times 10^{-27}\times 3.53 \times 10^7}{1.2 \times 1.6 \times 10^{-19}} \\\\Diameter = \frac{1.179 \times 10^{-19}}{1.92 \times 10^{-19}}[/tex]

Diameter = 0.614 meter

Read more on magnetic field here: https://brainly.com/question/12757739

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