Answer:
Electric force = 8.20x10⁻⁸ N
Gravitational force = 3.61x10⁻⁴⁷ N
Step-by-step explanation:
1. The electric force can be found using the following equation:
[tex] F_{e} = \frac{Kq_{e}q_{p}}{d^{2}} [/tex]
Where:
K: is the Coulomb's constant = 9x10⁹ N.m²/C²
[tex]q_{p}[/tex]: is the charge of the proton = 1.6x10⁻¹⁹ C
[tex]q_{e}[/tex]: is the charge of the electron = -1.6x10⁻¹⁹ C
d: is the distance = 5.3x10⁻¹¹ m
Hence, the magnitude of the electric force is:
[tex] |F_{e}| = \frac{9\cdot 10^{9} N.m^{2}/C^{2}*(-1.6\cdot 10^{-19} C)*1.6 \cdot 10^{-19} C}{(5.3 \cdot 10^{-11} m)^{2}} = 8.20 \cdot 10^{-8} N [/tex]
2. The gravitational force can be calculated as follows:
[tex] F_{g} = \frac{Gm_{e}m_{p}}{d^{2}} [/tex]
Where:
[tex]m_{e}[/tex]: is the electron's mass = 9.1x10⁻³¹ kg
[tex]m_{p}[/tex]: is the proton's mass = 1.67x10⁻²⁷ kg
G: is the gravitational constant = 6.67x10⁻¹¹ N.m²/kg²
Therefore, the gravitational force is:
[tex] F_{g} = \frac{6.67 \cdot 10^{-11} N.m^{2}/kg^{2}*9.1 \cdot 10^{-31} kg*1.67 \cdot 10^{-27} kg}{(5.3 \cdot 10^{-11} m)^{2}} = 3.61 \cdot 10^{-47} N [/tex]
As we can see, the gravitational force is much less than the electric force.
I hope it helps you!
