Answer:
The magnitude of the electric force is 0.27N, and the speed of the electron is 211,000,000 m/s, about 0.7c.
Explanation:
According to Coulomb's Law, we have that:
[tex]F_e=\frac{kq_1q_2}{r^2}\\\\F_e=\frac{(9*10^9Nm^2/C^2)26(1.6*10^{-19}C)(1.6*10^{-19}C)}{(1.5*10^{-13}m)^2}\\\\F_e=0.27N[/tex]
It means that the force of attraction between the nucleus and the electron is 0.27N.
Now, from the definition of centripetal force, we have:
[tex]F_e=\frac{m_ev^2}{r}\\\\\implies v=\sqrt{\frac{F_er}{m_e}}[/tex]
Considering that the mass of an electron is 9.1*10^-31 kg, and we know the magnitude of the electric force and the distance r, we can calculate the speed of the electron:
[tex]v=\sqrt{\frac{(0.27N)(1.5*10^{-13}m)}{9.1*10^{-31}kg}}\\\\v=211,000,000m/s[/tex]
Having that the speed of light is about 3*10^8 m/s, then the speed of the electron is 0.7c.
