Ask Question
12 December, 23:21

A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 T.

(a) What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d = 57 cm Previous

(b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?

+4
Answers (1)
  1. 12 December, 23:54
    0
    Given Information"

    Kinectic energy = 6.5 MeV

    magnetic field = B = 1.9 T

    Period = T = 1 ms

    Required Information"

    Diameter = d = ?

    Answer:

    d = 38.6 cm

    f = 1000

    Explanation:

    (a) What is the diameter of the largest orbit, just before the protons exit the cyclotron?

    The radius and hence the diameter of the largest orbit can be found by using

    r = mv / |q|B

    Where q = 1.60x10⁻¹⁹ C and m = 1.67x10⁻²⁷ kg and v is the speed of the particle which can be found by using

    v = √2K / m

    Where K is the kinetic energy in Joules.

    1 eV is equal to 1.60x10⁻¹⁹ J

    K = 6.5x10⁶*1.60x10⁻¹⁹ = 1.04x10⁻¹² J

    v = √2*1.04x10⁻¹² / 1.67x10⁻²⁷

    v = 35.29x10⁶ m/s

    r = 1.67x10⁻²⁷*35.29x10⁶ / 1.60x10⁻¹⁹*1.9

    r = 0.193 m

    d = 2r

    d = 2*0.193 = 0.386

    or d = 38.6 cm

    (b) A proton exits the cyclotron 1.0 ms after starting its spiral trajectory in the center of the cyclotron. How many orbits does the proton complete during this 1.0 ms?

    The period T and frequency (number of rotations per second) are related as

    f = 1/T

    f = 1/0.001

    f = 1000
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV. The magnetic field in the cyclotron is 1.9 ...” in 📙 Physics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers