Answer :
Answer:
Frequency, [tex]f=6.57\times 10^{15}\ Hz[/tex]
Explanation:
It is given that, the electron moves in a circular orbit of radius 0.053 nm around a stationary proton. The electric force acting on the electron is balanced by the centripetal force as :
[tex]\dfrac{kq^2}{r^2}=\dfrac{mv^2}{r}[/tex]
v is the speed of electron
[tex]v=\sqrt{\dfrac{ke^2}{mr}}[/tex]
[tex]v=\sqrt{\dfrac{9\times 10^9\times (1.6\times 10^{-19})^2}{9.1\times 10^{-31}\times 0.053\times 10^{-9}}}[/tex]
[tex]v=2.18\times 10^6\ m/s[/tex]
The speed of electron is given by :
[tex]v=\dfrac{2\pi r}{t}[/tex]
[tex]t=\dfrac{2\pi r}{v}[/tex]
[tex]t=\dfrac{2\pi \times 0.053\times 10^{-9}}{2.18\times 10^6}[/tex]
[tex]t=1.52\times 10^{-16}\ s[/tex]
We know that the number of revolutions per second is called frequency of electron. It is given by :
[tex]f=\dfrac{1}{t}[/tex]
[tex]f=\dfrac{1}{1.52\times 10^{-16}}[/tex]
[tex]f=6.57\times 10^{15}\ Hz[/tex]
So, the total number of revolutions per second make by the electron is [tex]f=6.57\times 10^{15}\ Hz[/tex]. Hence, this is required solution.