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 = Â 1.60 *10^{-19} \ Â 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]
=> Â Â Â [tex]d = Â 2 * Â 0.261[/tex]
=> Â Â Â [tex]d = Â 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]
=> Â Â [tex]T Â = \frac{2 * 3.142 Â * Â 1.672 *10^{-27} Â }{1.4 * Â 1.60 *10^{-19}}[/tex]
=> Â Â [tex]T Â = Â 4.691 *10^{-8} \ Â 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]
