Answer :
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]