Respuesta :
Answer:
The speed of the electron is [tex]3.178\times 10^7\ m/s[/tex].
Explanation:
Given:
Mass of electron is, [tex]m=9.11\times 10^{-31}\ kg[/tex]
Radius of circle is, [tex]R=2.00\times 10^{-2}\ m[/tex]
Force acting on the electron is, [tex]F=4.60\times 10^{-14}\ N[/tex]
Now, we know that, for a circular turn, the force acting on the electron is due to centripetal force. Centripetal force acting on the electron is given as:
[tex]F=\frac{mv^2}{R}[/tex]
Here, 'v' is the velocity of the electron.
Now, plug in all the given values and solve for 'v'. This gives,
[tex]4.60\times 10^{-14}=\frac{9.11\times 10^{-31}v^2}{2.00\times 10^{-2}}\\\\9.11\times 10^{-31}v^2=4.60\times 10^{-14}\times 2.00\times 10^{-2}\\\\9.11\times 10^{-31}v^2=9.2\times 10^{-16}\\\\v^2=\frac{9.2\times 10^{-16}}{9.11\times 10^{-31}}\\\\v^2=1.01\times 10^{15}\\\\v=\sqrt{1.01\times 10^{15}}\\\\v=3.178\times 10^7\ m/s[/tex]
Therefore, the speed of the electron is [tex]3.178\times 10^7\ m/s[/tex].
