Respuesta :
Answer:
(a): [tex]F_e = 8.202\times 10^{-8}\ \rm N.[/tex]
(b): [tex]F_g = 3.6125\times 10^{-47}\ \rm N.[/tex]
(c): [tex]\dfrac{F_e}{F_g}=2.27\times 10^{39}.[/tex]
Explanation:
Given that an electron revolves around the hydrogen atom in a circular orbit of radius r = 0.053 nm = 0.053[tex]\times 10^{-9}[/tex] m.
Part (a):
According to Coulomb's law, the magnitude of the electrostatic force of interaction between two charged particles of charges [tex]q_1[/tex] and [tex]q_2[/tex] respectively is given by
[tex]F_e = \dfrac{k|q_1||q_2|}{r^2}[/tex]
where,
- [tex]k[/tex] = Coulomb's constant = [tex]9\times 10^9\ \rm Nm^2/C^2.[/tex]
- [tex]r[/tex] = distance of separation between the charges.
For the given system,
The Hydrogen atom consists of a single proton, therefore, the charge on the Hydrogen atom, [tex]q_1 = +1.6\times 10^{-19}\ C.[/tex]
The charge on the electron, [tex]q_2 = -1.6\times 10^{-19}\ C.[/tex]
These two are separated by the distance, [tex]r = 0.053\times 10^{-9}\ m.[/tex]
Thus, the magnitude of the electrostatic force of attraction between the electron and the proton is given by
[tex]F_e = \dfrac{(9\times 10^9)\times |+1.6\times 10^{-19}|\times |-1.6\times 10^{-19}|}{(0.053\times 10^{-9})^2}=8.202\times 10^{-8}\ \rm N.[/tex]
Part (b):
The gravitational force of attraction between two objects of masses [tex]m_1[/tex] and [tex]m_1[/tex] respectively is given by
[tex]F_g = \dfrac{Gm_1m_2}{r^2}.[/tex]
where,
- [tex]G[/tex] = Universal Gravitational constant = [tex]6.67\times 10^{-11}\ \rm Nm^2/kg^2.[/tex]
- [tex]r[/tex] = distance of separation between the masses.
For the given system,
The mass of proton, [tex]m_1 = 1.67\times 10^{-27}\ kg.[/tex]
The mass of the electron, [tex]m_2 = 9.11\times 10^{-31}\ kg.[/tex]
Distance between the two, [tex]r = 0.053\times 10^{-9}\ m.[/tex]
Thus, the magnitude of the gravitational force of attraction between the electron and the proton is given by
[tex]F_g = \dfrac{(6.67\times 10^{-11})\times (1.67\times 10^{-27})\times (9.11\times 10^{-31})}{(0.053\times 10^{-9})^2}=3.6125\times 10^{-47}\ \rm N.[/tex]
The ratio [tex]\dfrac{F_e}{F_g}[/tex]:
[tex]\dfrac{F_e}{F_g}=\dfrac{8.202\times 10^{-8}}{3.6125\times 10^{-47}}=2.27\times 10^{39}.[/tex]
