Answer:
(a) [tex]F_g=1.62*10^{-48}N[/tex]
(b) [tex]F_e=3.68*10^{-9}N[/tex]
Explanation:
(a) We use Newton's law of universal gravitation, in order to calculate the gravitational force between electron and proton:
[tex]F_g=-G\frac{m_1m_2}{r^2}[/tex]
Where G is the Cavendish gravitational constant, [tex]m_1[/tex] and [tex]m_2[/tex] are the masses of the electron and the proton respectively and r is the distance between them:
[tex]F_g=-6.67*10^{-11}\frac{N\cdot m^2}{kg^2}\frac{(9.11*10^{-31}kg)(1.67*10^{-27}kg)}{(2.5*10^{-10}m)^2}\\F_g=-1.62*10^{-48}N[/tex]
The minus sing indicates that the force is repulsive. Thus, its magnitude is:
[tex]F_g=1.62*10^{-48}N[/tex]
(b) We use Coulomb's law, in order to calculate the electric force between electron and proton, here k is the Coulomb constant and e is the elementary charge:
[tex]F_e=-k\frac{e^2}{r^2}\\F_e=-8.99*10^{9}\frac{N\cdot m^2}{C^2}\frac{(1.6*10^{-19}C)^2}{(2.5*10^{-10}m)^2}\\F_e=-3.68*10^{-9}N[/tex]
Its magnitude is:
[tex]F_e=3.68*10^{-9}N[/tex]
