A medical cyclotron used in the production of medical isotopes accelerates protons to 6.5 MeV . The magnetic field in the cyclotron is 1.4 T . Part A What is the diameter of the largest orbit, just before the protons exit the cyclotron? Express your answer with the appropriate units. d d = nothing nothing SubmitRequest Answer Part 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 ? N N = nothing orbits SubmitRequest Answer Provide Feedback Next

Answers

Answer 1

Answer:

a

  The largest diameter is   [tex]d =  0.523 \ m [/tex]

b

The number of revolution is   [tex]n  =  2.132 *10^{4}[/tex]

Explanation:

From the question we are told that

   The kinetic energy of the electron is  [tex]K =  6.5 MeV =  6.5 *10^6 * 1.60 *10^{-19} = 1.04 *10^{-12} \  J[/tex]

    The magnetic field is  [tex]B  =  1.4 \  T[/tex]

       The time is  [tex]t =  1 ms =  1*0^{-3} \  s[/tex]

Generally the kinetic energy of the proton is mathematically represented as

           [tex]KE  =  \frac{1}{2}  *  m * v^2[/tex]

Here m is the mass of the  proton with a value  [tex]m = 1.672 *10^{-27} \  kg[/tex]

    =>  [tex]v  = \sqrt{ \frac{2 *  K }{ m} }[/tex]

=>      [tex]v  = \sqrt{ \frac{2 *  1.04 *10^{-12}  }{ 1.672 *10^{-27}} }[/tex]

=>      [tex]v  = 3.5271 * 10^{7} \  m/s [/tex]

Generally the radius of the largest orbit is mathematically represented as

       [tex]r =  \frac{ m *  v}{ B  *  e}[/tex]

Here e is the charge on a proton with the value [tex]e =  1.60 *10^{-19} \  C[/tex]

         [tex]r =  \frac{ 1.672 *10^{-27} * 3.5271 * 10^{7} }{  1.4  *    1.60 *10^{-19} }[/tex]

=> [tex]r = 0.261 \ m [/tex]

Generally the diameter is

     [tex]d =  2 *  r[/tex]

=>       [tex]d =  2 *  0.261[/tex]

=>       [tex]d =  0.523 \ m [/tex]

Gnerally the period of revolution round the orbit is mathematically represented as

       [tex]T  = \frac{2 \pi  *  m }{B  *  e}[/tex]

=>    [tex]T  = \frac{2 * 3.142  *  1.672 *10^{-27}  }{1.4 *  1.60 *10^{-19}}[/tex]

=>    [tex]T  =  4.691 *10^{-8} \  s [/tex]

Generally the number of revolution is mathematically represented as

      [tex]n  =  \frac{t}{T}[/tex]

     [tex]n  =  \frac{1*10^{-3}}{4.691 *10^{-8} }[/tex]

      [tex]n  =  2.132 *10^{4}[/tex]


Related Questions

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time period -1/10 frequency-10 hats

A ball is dropped from an upper floor, some unknown distance above Tom's apartment. As he looks out of his window, which is 1.10 m tall, Tom observes that it takes the ball 0.190 s to traverse the length of the window. Determine how high ℎ above the top of Tom's window the ball was dropped. Ignore the effects of air resistance.

Answers

Answer:

The height is 1.20 m above the window.

Explanation:

Given that,

Height of window = 1.10 m

Time = 0.190 sec

We need to calculate the velocity

Using equation of motion

[tex]s=ut+\dfrac{1}{2}gt^2[/tex]

Put the value into the formula

[tex]1.10=u\times0.190+\dfrac{1}{2}\times9.8\times(0.190)^2[/tex]

[tex]1.10=u\times0.190+0.17689[/tex]

[tex]u=\dfrac{1.10-0.17689}{0.190}[/tex]

[tex]u=4.85\ m/s[/tex]

We need to calculate the height

Using equation of motion

[tex]v^2=u^2+2gh[/tex]

Put the value into the formula

[tex](4.85)^2=0+2\times9.8\times h[/tex]

[tex]h=\dfrac{(4.85)^2}{2\times9.8}[/tex]

[tex]h=1.20\ m[/tex]

Hence, The height is 1.20 m above the window.

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Answers

Answer:

0.004

Explanation:

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Answers

Answer:

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Answers

Answer:

324 in ===

Explanation:

Answer:

36 kg

Explanation:

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v= 9 m/s

m= 324 / 9

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Answers

Answer:

Please find the answer in the explanation

Explanation:

Friction is a force that opposes motion. One or two of the advantages of friction are break and ability of an object to walk.

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Answers

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Answer:

0.31429 Amps

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In a circuit, a variable resistor is to be connected across a potential difference of 60 volts to allow the current to be adjusted in the range from 40 milliamperes to 100 milliamperes.
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Answer:

600 and 1500 [ohm

Explanation:

To solve this problem we must use ohm's law, which tells us that the voltage is the product of the current by the resistance, so we have:

V = I*R

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R2 = 60/(100*10^-3) = 600 [ohm]

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Answers

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Answer:

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Answer:

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Explanation:

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Answers

Answer:

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Explanation:

Horizontal Motion

When an object is thrown horizontally with a speed v from a height h, it describes a curved trajectory ruled by a constant speed in the horizontal direction and a variable speed in the vertical direction, where the acceleration of gravity makes the object fall to the ground.

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