The distance between the proton and the electron in a hydrogen atom is 5.3 × 10⁻¹¹ m. Determine:
a) The intensity of gravitational force between proton and electron;
b) The intensity of electric force between proton and electron;
c) Compare the two forces.
Consider the following values:
mass of proton:   \( m_p=1.7\times 10^{-27}\;\mathrm{kg} \) ;
mass of electron:   \( m_e=9.1\times 10^{-31}\;\mathrm{kg} \) ;
universal gravitational constant:    \( G=6.67\times 10^{-11}\;\mathrm{\frac{N.m^2}{kg^2}} \) ;
charge of a proton:   \( q_p=1.6\times 10^{-19}\;\mathrm C \) ;
charge of an electron:   \( q_e=-1.6\times 10^{-19}\;\mathrm C \) ;
Coulomb constant:   \( k_e=9\times 10^9\;\mathrm{\frac{N.m^2}{C^2}} \) .

Two positive point charges, of which one is triple the other, repel with magnitude force 2.7 N in the vacuum when the distance between them is 10 cm. Determine the charge of the small value. Coulomb constant   \( k_e=9\times 10^9\;\mathrm{\frac{N.m^2}{C^2}} \).

The hydrogen atom is made up of one proton and one electron. According to Bohr's atomic model, the electron follows a circular trajectory with the proton in the center.
Data:
electron mass:   \( 9.1\times 10^{-31}\;\mathrm{kg} \) ;
electron speed:   \( 2.2\times 10^\;\mathrm C \) ;
proton charge:   \( 1.6\times 10^{-19}\;\mathrm C \) ;
electron charge:   \( -1.6\times 10^{-19}\;\mathrm C \) .
Determine the radius of the orbit of an electron for the atom in a vacuum.