Respuesta :
Answer:
The radius of the electron's path and the frequency of the motion are [tex]9.44\times10^{-5}\ m[/tex] and [tex]3.06\times10^{5}\ Hz[/tex].
Explanation:
Given that,
Magnetic field = 0.0000109 T
Speed = 181 m/s
We need to calculate the radius of the electron
Using formula of radius
[tex]r = \dfrac{mv}{qB}[/tex]
Where, m = mass
v = velocity
q = charge
B = magnetic field
Put the value into the formula
[tex]r=\dfrac{9.1\times10^{-31}\times181}{1.6\times10^{-19}\times 0.0000109}[/tex]
[tex]r=9.44\times10^{-5}\ m[/tex]
We calculate the time
Using formula of time
[tex]t=\dfrac{d}{v}[/tex]
Distance is the circumference.
[tex]t=\dfrac{2\pi r}{v}[/tex]
Put the value into the formula
[tex]t=\dfrac{2\times\pi\times9.44\times10^{-5}}{181}[/tex]
[tex]t=3.27\times10^{-6}\ s[/tex]
We need to calculate the frequency
The frequency is the inverse of the time for one revolution.
[tex]f=\dfrac{1}{t}[/tex]
Put the value of t into th formula
[tex]f=\dfrac{1}{3.27\times10^{-6}}[/tex]
[tex]f=3.06\times10^{5}\ Hz[/tex]
Hence, The radius of the electron's path and the frequency of the motion are [tex]9.44\times10^{-5}\ m[/tex] and [tex]3.06\times10^{5}\ Hz[/tex].
