Explanation:
It is given that,
Radius of orbit, [tex]r=0.55\times 10^{-10}\ m[/tex]
Charge on electron, [tex]q=1.6\times 10^{-19}\ C[/tex]
(a) The electric force exerted on each particle is given by :
[tex]F=k\dfrac{q^2}{r^2}[/tex]
[tex]F=9\times 10^9\times \dfrac{(1.6\times 10^{-19})^2}{(0.55\times 10^{-10})^2}[/tex]
[tex]F=7.61\times 10^{-8}\ N[/tex]
(b) If this force causes the centripetal acceleration of the electron, then we need to find the speed of the electron. Let v is the speed,
So, [tex]F=\dfrac{mv^2}{r}[/tex]
[tex]v=\sqrt{\dfrac{Fr}{m}}[/tex]
[tex]v=\sqrt{\dfrac{7.61\times 10^{-8}\times 0.55\times 10^{-10}}{9.1\times 10^{-31}}}[/tex]
v = 2144632.96 m/s
or
[tex]v=2.14\times 10^6\ m/s[/tex]
Hence, this is the required solution.
